ഽ\(\frac { 1 }{ { x }^{ 3 } } \)dx is _______.

(a)

\(\frac { -3 }{ { x }^{ 2 } } +c\)

(b)

\(\frac { -1 }{ 2{ x }^{ 2 } } +c\)

(c)

\(\frac { -1 }{ { 3x }^{ 2 } } +c\)

(d)

\(\frac { -2 }{ { x }^{ 2 } } +c\)

\(\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x\) is _______.

(a)

−cos 2x + c

(b)

−cos 2x + c

(c)

\(-\frac14\)cos2x + c

(d)

−4cos2x + c

ഽ\(\sqrt { { e }^{ x } } \) dx is _______.

(a)

\(\sqrt { { e }^{ x } } +c\)

(b)

\(2\sqrt { { e }^{ x } } \) + c

(c)

\(\frac12\sqrt { { e }^{ x } } +c\)

(d)

\(\frac { 1 }{ 2\sqrt { { e }^{ x } } } +c\)

\(\Gamma (n)\) is _______.

(a)

(n −1)!

(b)

n!

(c)

\(n\Gamma (n)\)

(d)

(n −1)\(\Gamma \)(n)

\(\int { \left( x-1 \right) } { e }^{ -x }\) dx = __________ +c

(a)

-xe^x

(b)

xe^x

(c)

-xe^-x

(d)

xe^-x

∫ e^-t dt

(1)

(n - 1) \(\Gamma \)
(n - 1), n > 1

\(\int _{ 0 }^{ \infty }{ { e }^{ -t } } dt\quad \)

(2)

n! where n is a positive integer

\(\Gamma (n)\quad \)

(3)

Improper definite intgral

\(\Gamma \) (n + 1)

(4)

Indefinite inegral

\(\Gamma \) (n + 1)

(5)

n \(\Gamma \) (n), n > 0

Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)

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

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

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

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

Evaluate \(\int \sqrt{2 x+1} \ d x\)

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

Evaluate \(\int { } \)x³ logx dx

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

Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ { x }^{ 2 } } \) dx

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

Evaluate \(\int { { sin }^{ 2 }xdx } \)

Evaluate \(\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 3 } }{ \sin x } \) dx

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

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