How do you integrate $\int cos (2 x + 1)$ $int cos(2x+1)$ using substitution?

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How do you integrate $\int cos (2 x + 1)$ $int cos(2x+1)$ using substitution?

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Answer 1 · 2017-01-12T15:52:50

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

Explanation:

Substitute:

$t = 2 x + 1$ $t=2x+1$
$d t = 2 d x$ $dt= 2dx$

and you have:

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

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How do you integrate $\int cos (2 x + 1)$ $int cos(2x+1)$ using substitution?

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How do you integrate $\int cos (2 x + 1)$ $int cos(2x+1)$ using substitution?