\(\int { { 3 }^{ x+2 } } \) dx = __________+c.

(a)

\(\frac { { 3 }^{ x } }{ log3 } \)

(b)

\(9\left( \frac { { 3 }^{ x } }{ log3 } \right) \)

(c)

\(\frac { { 3 }^{ x } }{ 9log3 } \)

(d)

3^x.9

\(\int { \frac { sin\sqrt { x } }{ x } } \) dx = ________ +c.

(a)

2 cos \(\sqrt { x } \)

(b)

2 sin \(\sqrt { x } \)

(c)

-2 sin \(\sqrt { x } \)

(d)

-2 cos \(\sqrt { x } \)

\(\int { \frac { 1 }{ 9x^{ 2 }-4 } } \) dx = ________+c.

(a)

log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(b)

\(\frac { 1 }{ 12 } \)log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(c)

12log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(d)

\(\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right| \)

\(\int { \frac { x }{ 4+{ x }^{ 4 } } } \) dx is equal to________+c.

(a)

\(\frac { 1 }{ 4 } \) tan^-1 (x²)

(b)

\(\frac { 1 }{ 4 } \) tan^-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

(c)

\(\frac { 1 }{ 2 } \) tan^-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

(d)

none of these

\(\int { { e }^{ x }\left[ f\left( x \right) +f'\left( x \right) \right] } \) dx = ___________+c.

(a)

e^x f (x)

(b)

e^x f (x)

(c)

2e^x f(x)

(d)

e^x - f (x)