Evaluate \(\int { { a }^{ 3{ log }_{ a }x } } dx\)

Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)

Evaluate ∫ tan²x dx

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

Evaluate \(\int { \frac { { 2 }^{ x }+{ 3 }^{ x } }{ { 5 }^{ x } } dx } \)

If f'(x) = 8x³ -2x², f(2) = 1, find f(x)

Evaluate \(\int { x } \sqrt { x+2 } dx\)

If \(\int _{ 0 }^{ 1 }{ \left( { 3x }^{ 2 }+2x+k \right) } dx=0\), find k.

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

If \(\int _{ 0 }^{ a }{ { 3x }^{ 2 } } dx=8\) find the value of a

Evaluate the following integrals:
\(\int a^{3} \log _{d} x d x\)

\(\int \frac{e^{5 \log _{e} x}-e^{+\log _{1} x}}{e^{3 \log _{e} x}-e^{2 \log _{1} x}} d x\)

\(\int \frac{2}{1+\cos 2 x} d x\)

\(\int \frac{2 d x}{1-\cos 2 x}\)

\(\int e^{a \log _{x} x} d x\)