Indefinite Integration · Mathematics · BITSAT

The value of $$\int {{1 \over {{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{{1 \over 4}}}}}dx} $$, is

Let $$f(x) = \int {{{{x^2}dx} \over {(1 + {x^2})(1 + \sqrt {1 + {x^2}} )}}} $$ and $$f(0) = 0$$, then the value of $$f(1)$$ be

$$\int {{1 \over {1 - 2\sin x}}dx} $$ is equal to

$$\int {{{8{x^{43}} + 13{x^{38}}} \over {{{({x^{13}} + {x^5} + 1)}^4}}}dx} $$ equals to