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)

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

ഽ\(\frac{logx}{x}\) dx , x > 0 is _______.

(a)

\(\frac12\)(log x)² + c

(b)

-\(\frac12\)(log x)²

(c)

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

(d)

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

ഽ\(\left[ \frac { 9 }{ x-3 } -\frac { 1 }{ x+1 } \right] \)dx is _______.

(a)

\(log\left| x-3 \right|-log \left| x+1 \right| +c\)

(b)

\(log\left| x-3 \right|+log \left| x+1 \right| +c\)

(c)

\(9log\left| x-3 \right|-log \left| x+1 \right| +c\)

(d)

\(9log\left| x-3 \right|+log \left| x+1 \right| +c\)

\(\int _{ 0 }^{ 1 }{ (2x+1) } dx\) is _______.

(a)

1

(b)

2

(c)

3

(d)

4

\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \) dx is _______.

(a)

1

(b)

2\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \)dx

(c)

0

(d)

\({ e }^{ { x }^{ 4 } }\)

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

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

Integrate the following with respect to x.
\(\sqrt { 1-\sin2x } \)

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

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

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

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

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