Question #1b237

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Answer 1 · 2017-03-27T19:41:45

Use $cos(2x) = 1-2sin^2x$ to rewrite.

$sin^2x = 1/2(1-cos(2x))$
(this is called a Power Reduction Formula)

So,

$int sin^2x dx = 1/2int (1-cos(2x)) dx$

We can integrate $intcos(2x) dx$ by substitution $u = 2x$

so $intcos(2x) dx = 1/2sin(2x) +C$ (check this answer by differentiation)

$int sin^2x dx = 1/2int (1-cos(2x)) dx$

$= 1/2(x-1/2sin(2x))+C$

Rewrite to taste.