How do you find the integral $int cos(2x+1)dx$ using substitution?

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Answer 1 · 2018-04-14T03:57:07

$intcos(2x+1)dx=1/2sin(2x+1)+C$

$u=2x+1$

$(du)/dx=2$

$du=2dx$

Solve for $dx,$ yielding

$1/2du=dx$

Then, using the substitution and factoring the constant out, we have

$1/2intcosudu=1/2sinu+C$

Rewriting in terms of $x$ yields

$intcos(2x+1)dx=1/2sin(2x+1)+C$

How do you find the integral int cos(2x+1)dxint cos(2x+1)dx using substitution?