Write an anti derivative for each of the followings functions, using method of inspection :
(i) \(\cos { 2x } \)     
(ii) \({ 3x }^{ 2 }+{ 4x }^{ 3 }\)     
(iii)  \(\frac { 1 }{ x } ,x\neq 0\)

3

(a)

Find the following integrals:
\((i)\int { \frac { { x }^{ 3 }-1 }{ { x }^{ 2 } } } dx\)
\((ii) \int\left(x^{\frac{2}{3}}+1\right) d x\)
\((iii) \int\left(x^{\frac{3}{2}}+2 e^x-\frac{1}{x}\right) d x\)

3

(a)

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

3

(a)

Find: \(\int { \frac { { x }^{ 2 } }{ ({ x }^{ 2 }+1)({ x }^{ 2 }+4) } } dx\)

3

(a)

Find:\(\int { \sqrt { 3-2x-{ x }^{ 2 } } } dx.\)

3

(a)

Find:\(\int { \frac { { x }^{ 4 } dx }{ { (x }-1)({ x }^{ 2 }+1) } }\)

3

(a)

Find:\(\int { \frac { \sin { 2x } \cos { 2x }\space dx}{ \sqrt { 9-\cos ^{ 4 }{ (2x) } } } }\)

3

(a)

Find an anti derivative (or integral) of the following by the method of inspection \({ e }^{ 2x }\)

3

(a)

Find an anti derivative (or integral) of the following by the method of inspection \((ax+{ b) }^{ 3 }\)

3

(a)

Find the integral: \(\int { \sqrt { x } } \left( { 3x }^{ 2 }+2x+3 \right) dx.\)

3

(a)

Find the integral : \(\int { \left( 2x-3\cos { x } +{ e }^{ x } \right) } dx\)

3

(a)

If \(\frac { d }{ dx } f\left( x \right) ={ 4x }^{ 3 }-\frac { 3 }{ { x }^{ 4 } } \)such that f(2) = 0, then f(x) is:
\((a)\quad { x }^{ 4 }+\frac { 1 }{ { x }^{ 2 } } -\frac { 129 }{ 8 } \)
\((b)\quad { x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } +\frac { 129 }{ 8 } \)
\((c)\quad { x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } +\frac { 129 }{ 8 } \)
\((d)\quad { x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } -\frac { 129 }{ 8 } \)

3

(a)

Integrate  \(\frac { 2x }{ 1+{ x }^{ 2 } } .\)

3

(a)

Integrate  \(\frac { 1 }{ x+x\log { x } } \)

3

(a)

Integrate \(\sin { (ax+b) } \cos { (ax+b) } \)

3

(a)