Evaluate \(\int \frac{a x^{2}+b x+c}{\sqrt{x}} d x\)

Evaluate \(\int { \frac { { 2x }^{ 2 }-14x+24 }{ x-3 } dx } \)

Evaluate \(\int { \frac { x+2 }{ \sqrt { 2x+3 } } } dx\)

Evaluate \(\int { \frac { 1 }{ \sqrt { x+2 } -\sqrt { x-2 } } } dx\)

 Integrate the following with respect to x.
\(\sqrt{x}\)(x³ − 2x + 3)

Integrate the following with respect to x.
\(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)

 Integrate the following with respect to x.
\(\frac { 1 }{ \sqrt { x+1 } +\sqrt { x-1 } } \)

If f'(x) = x + b, f(1)= 5 and f(2) = 13, then find f(x)

If f '(x) = 8x³ − 2x and f(2) = 8, then find f(x)

Evaluate  \(\int { \frac { { x }^{ 2 }+2x+3 }{ x+1 } dx}\)

Evaluate \(\int \frac{x^{3}+5 x^{2}-9}{x+2} d x\)

Evaluate \(\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx } \)

Integrate the following with respect to x.
\(\frac { { x }^{ 4 }-{ x }^{ 2 }+2 }{ x-1 } \)

Integrate the following with respect to x.
\(\frac { { x }^{ 3 } }{ x+2 } \)

Integrate the following with respect x.
\(\frac { { x }^{ 3 }+3x^{ 2 }-7x+11 }{ x+5 } \)

Integrate the following with respect x
\(\frac { 3x+2 }{ \left( x-2 \right) \left( x-3 \right) } \)

Integrate the following with respect to x.
If f' x = 1/x and f(1) = π/4, then find f(x).

Evaluate \(\int { \frac { { 5+5e }^{ 2x } }{ { e }^{ x }+{ e }^{ -x } } dx } \)

Integrate the following with respect to x.
e^{x log a} + e^{a log a} − e^{nlog x}

Integrate the following with rexpect to x
\(\frac { { a }^{ x }-{ e }^{ xlogb } }{ { e }^{ xloga }{ b }^{ x } } \)

Integrate the following with respect to x.
(e^x +1)² e^x

Integrate the following with respect to x.
\(\frac { { e }^{ 3x }-{ e }^{ -3x } }{ { e }^{ x } } \)

Integrate the following with respect to x.
\(\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } } \)

Integrate the following with respect to x.
\(\left[ 1-\frac { 1 }{ { x }^{ 2 } } \right] { e }^{ \left( x+\frac { 1 }{ x } \right) }\)

Integrate the following with respect to x.
\(\frac { 1 }{ x{ \left( \log x \right) }^{ 2 } } \)

If f′(x) = e^x and f(0) = 2, then find f(x)

Evaluate  \(\int { } \)cos³ x dx

Integrate the following with respect to x.
sin³ x

Integrate the following with respect to x.
\(\frac { { \cos 2x+2 \sin }^{ 2 }x }{ { \cos }^{ 2 }x } \)

Integrate the following with respect to x.
\(\frac { 1 }{ { \sin }^{ 2 }x{ \cos }^{ 2 }x } [Hint:\sin ^{ 2 }+{ \cos }^{ 2 }x=1]\)

Evaluate \(\int { } \)xe^x dx

Evaluate \(\int { } \)x³e^xdx

Evaluate \(\int { } \)x³ logx dx

Evaluate \(\int { \left( { x }^{ 2 }-2x+5 \right) } { e }^{ -x }dx\)

Integrate the following with respect to x.
xe^−x

Integrate the following with respect to x.
x³e^3x

Integrate the following with respect to x.
log x

Integrate the following with respect to x.
x log x

Integrate the following with respect to x.
xⁿ log x

Integrate the following with respect to x.
\(x^{ 5 }{ e }^{ { x }^{ 2 } }\)

Evaluate \(\int { \frac { { x }^{ 3 } }{ { \left( { x }^{ 2 }+1 \right) }^{ 3 } } dx } \)

Evaluate \(\int { \frac { dx }{ x\left( { x }^{ 3 }+1 \right) } } \)

Evaluate \(\int { { x }^{ 3 }{ e }^{ { x }^{ 2 } }dx } \) 

Evaluate \(\int { { e }^{ x }\left( { x }^{ 2 }+2x \right) dx } \)

Evaluate ഽe^2x\(\left[ \frac { 2x-1 }{ { 4x }^{ 2 } } \right] \)dx

Integrate the following with respect to x.
\(\frac { { e }^{ 3logx } }{ { x }^{ 4 }+1 } \)

Integrate the following with respect to x.
\(\frac { (\log x)^{ 3 } }{ x } \)

Integrate the following with respect to x.
\(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

Integrate the following with respect to x.
\({ e }^{ x }\left[ \frac { 1 }{ { x }^{ 2 } } -\frac { 2 }{ { x }^{ 3 } } \right] \)

Integrate the following with respect to x.
\({ e }^{ 3x }\left[ \frac { 3x-1 }{ { 9x }^{ 2 } } \right] \)

Evaluate ഽ \(\frac { dx }{ 2+x-{ x }^{ 2 } } \)

Evaluate ഽ\(\frac { { x }^{ 2 } }{ { x }^{ 2 }-25 } \)dx

Evaluate ഽ\(\frac { dx }{ x^{ 2 }-3x+2 } \)

Evaluate ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }-3x+2 } } \)

Evaluate ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }+4x+8 } } \)

Evaluate ഽ\(\frac { { x }^{ 3 }dx }{ \sqrt { x^{ 8 }+1 } } \) 

Evaluate ഽ\(\sqrt { x^{ 2 }-4x+3 } \) dx

Evaluate ഽ\(\frac { 1 }{ x-\sqrt { { x }^{ 2 }-1 } } \) dx

Integrate the following with respect to x
\(\frac { 1 }{ { 9-8x-x }^{ 2 } } \)

Integrate the following with respect to x
\(\frac { 1 }{ { x }^{ 2 }-x-2 } \)

Integrate the following with respect to x
\(\frac { 1 }{ { x }^{ 2 }+3x+2 } \)

Integrate the following with respect to x
\(\frac { { 1 } }{ { 2x }^{ 2 }+6x-8 } \)

Integrate the following with respect to x
\(\frac { { e }^{ x } }{ { e }^{ 2x }-9 } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }+6x+13 } } \)

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }-3x+2 } } \)

Integrate the following with respect to x
\(\frac { { x }^{ 3 } }{ \sqrt { { x }^{ 8 }-1 } } \)

Integrate the following with respect to x
\(\sqrt { { 1+x+x }^{ 2 } } \)

Integrate the following with respect to x
\(\sqrt { { 2x }^{ 2 }+4x+1 } \)

Integrate the following with respect to x
\(\frac { 1 }{ x+\sqrt { { x }^{ 2 }-1 } } \)

Evaluate \(\int _{ 0 }^{ 1 }{ ({ x }^{ 3 }+7{ x }^{ 2 }-5x) } \) dx

Find the integration for \(\frac { dy }{ dx } =\frac { 2x }{ { 5x }^{ 2 }+1 } \) with limiting values as 0 and 1

Evaluate \(\int _{ 0 }^{ 1 }{ ({ e }^{ x }-{ 4a }^{ x }+2+\sqrt [ 3 ]{ x } } )dx\)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { cos }^{ 2 }xdx } \)

Evaluate \(\int _{ 0 }^{ 1 }{ [{ e }^{ a \log x }+{ e }^{ x \log a }] } dx\)

Evaluate \(\int _{ -1 }^{ 1 }{ { ({ x }^{ 3 }+{ 3x }^{ 2 }) }^{ 3 } } \) (x² +  2x)dx

Evaluate \(\int _{ a }^{ b }{ \frac { \sqrt { \log x } }{ x } dx } \) a, b > 0

Evaluate \(\int _{ -1 }^{ 1 }{ x\sqrt { x+1 } } dx\)

Evaluate \(\int _{ 0 }^{ \infty }{ { x }^{ 2 } } { e }^{ { -x }^{ 3 } }dx\)

Evaluate \(\int _{ 1 }^{ 2 }{ \frac { 1 }{ (x+1)(x+2) } } dx\)

Evaluate \(\int _{ 1 }^{ e }{ \log x } \) dx

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }\) x sin x dx

If \(\int _{ a }^{ b }{ dx } =1\) and \(\int _{ a }^{ b }{ xdx } =1\), then find a and b

Evaluate \(\int _{ 1 }^{ 4 }{ f(x) } dx\), where f(x) = \(\begin{cases} 7x+3,if \ 1\le x\le 3 \\ 8x,if \ 3\le x\le 4 \end{cases}\)

Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ 2 }{ \frac { xdx }{ { x }^{ 2 }+1 } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 1 }{ { xe }^{ { x }^{ 2 } } } \) dx

Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ e }{ \frac { dx }{ x(1{ +logx) }^{ 3 } } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ -1 }^{ 1 }{ \frac { 2x+3 }{ { x }^{ 2 }+3x+7 } dx } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sqrt { 1+ \cos x } dx } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ 2 }{ \frac { x-1 }{ { x }^{ 2 } } dx } \)

Evaluate the following:
\(\int _{ 1 }^{ 4 }{ f(x) } dx\) where f(x) = \(\begin{cases} 4x+3, \\ 3x+5, \end{cases}\begin{matrix} 1 & \le & x \\ 2 & \le & x \end{matrix}\begin{matrix} \le & 2 \\ \le & 4 \end{matrix}\)

Evaluate the following:
\(\int_{0}^{2} f(x) d x \)where f (x)= \(\begin{cases} 3-2 x-x^{2}, x \leq 1 \\ x^{2}+2 x-3,1, \end{cases}\begin{matrix} \\ \end{matrix}\)

Evaluate the following:
\(\int _{ -1 }^{ 1 }{ f(x) } dx\)  where f(x) = \(\begin{cases} x, \\ -x, \end{cases}\begin{matrix} x & \ge & 0 \\ x & < & 0 \end{matrix}\)

Evaluate the following: f(x) = \(\begin{cases} cx, \\ 0, \end{cases}\begin{matrix} 0 < x < 1 \\ \text{otherwise} \end{matrix}\)

Evaluate the following using properties of definite integrals:
\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^{2} \theta d \theta\)

Evaluate the following using properties of definite integrals:
\(\int _{ -1 }^{ 1 }{ \log\left( \frac { 2-x }{ 2+x } \right) } dx\)

\(If \ f(x)=\left\{\begin{array}{l}x^{2} e^{-2 x}, x \geq 0 \\ 0, \text { otherwise }\end{array}\right., then \ evaluate \int_{0}^{\infty} f(x) d x\)

Evaluate the following integrals:
ഽ\(\frac { 1 }{ \sqrt { x+2 } -\sqrt { x+3 } } \)dx

Evaluate the following integrals:
ഽ\(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

Evaluate the following integrals:
ഽ\(\frac { dx }{ { e }^{ x }+6+{ 5e }^{ -x } } \)

Evaluate the following integrals:
ഽ\(\sqrt { 9{ x }^{ 2 }+12x+3 } \) dx

Evaluate the following integrals:
ഽ(x +1)² log x dx

Evaluate the following integrals:
ഽ log(x −\(\sqrt { { x }^{ 2 }-1 } \)) dx

Evaluate the following integrals:
\(\int _{ 0 }^{ 1 }{ \sqrt { x(x-1) } } \) dx

Evaluate the following integrals:
\(\int _{ -1 }^{ 1 }{ { x }^{ 2 }{ e }^{ -2x } } dx\)

Evaluate the following
\(\int _{ 0 }^{ \infty }{ { e }^{ -\frac { x }{ 2 } } } { x }^{ 5 }dx\)

Evaluate
\(\int _{ 0 }^{ \infty }{ { e }^{ -{ x }^{ 2 } } } dx\)

If f(x) = \(\begin{cases} { x }^{ 2 }, \\ x, \\ x-4, \end{cases}\begin{matrix} -2 & \le & x \\ 1 & \le & x \\ 2 & \le & x \end{matrix}\begin{matrix} < & 1 \\ < & 2 \\ \le & 4 \end{matrix}\), then find the following
(i) \(\int _{ -2 }^{ 1.5 }{ f(x) } dx\)
(ii) \(\int _{ 1 }^{ 3 }{ f(x) } dx\)

Evaluate \(\int_{2}^{3} \frac{x^{4}+1}{x^{2}} d x\)