Integral of $int x/sin^2(x^2)dx$ ?

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Answer 1 · 2018-06-27T16:13:11

$int x/sin^2(x^2)dx = -1/2cot(x^2) + c$

Let $u = x^2$ , then $1/2u = xdx$ :

$1/2int 1/sin^2(u)du$

Substitute $1/sin^2(u) = csc^2(u)$ :

$1/2int csc^2(u)du$

$-1/2cot(u) + c$

Reverse the substitution:

$int x/sin^2(x^2)dx = -1/2cot(x^2) + c$

Integral of int x/sin^2(x^2)dxint x/sin^2(x^2)dx?