5x-2-cos-2x-dx-

Question Number 168296 by Florian last updated on 07/Apr/22

\int (5 x + 2) c o s (2 x) d x = ?

Answered by floor(10²Eta[1]) last updated on 07/Apr/22

u = 5 x + 2 \Rightarrow du = 5 dx

dv = \cos (2 x) dx \Rightarrow v = \frac{\sin (2 x)}{2}

= \frac{(5 x + 2) \sin (2 x)}{2} - \frac{5}{2} \int \sin (2 x) dx

= \frac{(5 x + 2) \sin (2 x)}{2} + \frac{5 \cos (2 x)}{4} + C

Commented by Florian last updated on 08/Apr/22

C o r r e c t!

Answered by peter frank last updated on 07/Apr/22

\int 5 xcos 2 xdx + \int 2 \cos 2 xdx

5 \int xcos xdx + 2 \int \cos 2 xdx

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