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

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Answer 1 · 2018-04-14T03:57:07

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

$u = 2 x + 1$ $u=2x+1$

$\frac{d u}{d x} = 2$ $(du)/dx=2$

$d u = 2 d x$ $du=2dx$

Solve for $d x,$ $dx,$ yielding

$\frac{1}{2} d u = d x$ $1/2du=dx$

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

$\frac{1}{2} \int cos u d u = \frac{1}{2} sin u + C$ $1/2intcosudu=1/2sinu+C$

Rewriting in terms of $x$ $x$ yields

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

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