Evaluate  \(\int { \frac { { { x }^{ 4 }+{ x }^{ 4 }+1 } }{ { x }^{ 2 }-x+1 } } \)

Evaluate \(\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx\)

Evaluate \(\int { \frac { { ({ a }^{ x }{ +b }^{ x }) }^{ 2 } }{ { a }^{ x }b^{ x } } dx } \)

If f' (x) = 3x² - \(\frac { 2 }{ { x }^{ 3 } } \) and f(1) = 0, find f(x)

Evaluate \(\int { \frac { { 8 }^{ 1+x }+{ 4 }^{ 1-x } }{ { 2 }^{ x } } } dx\)

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

Evaluate ഽ sin³ x cos x dx

Evaluate \(\int { \frac { 1 }{ \sqrt { { 16x }^{ 2 }+25 } } } dx\)

Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)

Evaluate \(\int _{ 1 }^{ 2 }{ \frac { log\quad x }{ { x }^{ 2 } } } dx\)

\(\int_{0}\left(x^{2}-\frac{1}{x^{2}}\right)^{3} d x \)

\(\int\left(e^{x \log a } + e^{a {\log } x} + e^{a \log a }\right) d x\)

\(\int\left(\frac{x}{m} + \frac{m}{x} + x^{m} + m^{2}\right) d x\)

If \(f^{\prime}(x)=3 x^{2}-\frac{2}{x^{3}}\) and f(1) = 0, find f(x).

Write the primitive or antiderivative of \(f(x)=\sqrt{x}-\frac{1}{\sqrt{x}}\)