\(\int { { \left| x \right| }^{ 3 } } \)dx = ________________ +c

(a)

\(\frac { { -x }^{ 4 } }{ 4 } \)

(b)

\(\frac { { \left| x \right| }^{ 4 } }{ 4 } \)

(c)

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

(d)

none of these

\(\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } } \) dx = ____________ +c 

(a)

\(\frac { { -e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } \)

(b)

\(-\frac { { -e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } \)

(c)

\(\frac { 1 }{ { \left( { e }^{ x }+1 \right) }^{ 2 } } \)

(d)

\(\frac { 1 }{ { e }^{ x }-{ e }^{ -x } } \)

\(\int { { e }^{ x } } \) (1-cot x +cot² x) dx = _______________ +c

(a)

e^x cot x

(b)

- e^x cot x

(c)

e^x cosec x

(d)

-e^x cosec x

\(\int { { e }^{ x } } \) f(x) + f' (x) dx = _____________ +c

(a)

e^x f(x)

(b)

e^x + f(x)

(c)

2e^x f(x)

(d)

e^x - f(x)

If ∫ x sin x dx = - x cos x + α then α = __________ +c

(a)

sin x

(b)

cos x

(c)

C

(d)

none of these