How do you find the general antiderivative of $f (x) = sin 2 x + cos 2 x$ $f(x)= sin2x+cos2x$ ?

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Answer 1 · 2015-02-25T19:42:42

The answer is: $- \frac{1}{2} cos 2 x + \frac{1}{2} sin 2 x + c$ $-1/2cos2x+1/2sin2x+c$ .

This is because:

$\int (sin 2 x + cos 2 x) d x = \frac{1}{2} \int (2 sin 2 x + 2 cos 2 x) d x =$ $int(sin2x+cos2x)dx=1/2int(2sin2x+2cos2x)dx=$

$= - \frac{1}{2} cos 2 x + \frac{1}{2} sin 2 x + c$ $=-1/2cos2x+1/2sin2x+c$ ,

using these rules:

$intsinf(x)*f'(x)dx=-cosf(x)+c$

and

$intcosf(x)*f'(x)dx=sinf(x)+c$

How do you find the general antiderivative of f(x)= sin2x+cos2xf(x)=sin2x+cos2xf(x)= sin2x+cos2x?