What is the integral of cos(2x+1)x ?

The integral of cos(2x+1)x is 1/2 xsin(2x+1)+1/4 cos(2x+1)+C

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integral of cos(2x+1)x

\int cos (2 x + 1) x d x

\frac{1}{2} x sin (2 x + 1) + \frac{1}{4} cos (2 x + 1) + C

Solution steps

\int cos (2 x + 1) x d x

Apply Integration By Parts

: \frac{1}{2} x sin (2 x + 1) - \int \frac{1}{2} sin (2 x + 1) d x

= \frac{1}{2} x sin (2 x + 1) - \int \frac{1}{2} sin (2 x + 1) d x

\int \frac{1}{2} sin (2 x + 1) d x = - \frac{1}{4} cos (2 x + 1)

= \frac{1}{2} x sin (2 x + 1) - (- \frac{1}{4} cos (2 x + 1))

Simplify

= \frac{1}{2} x sin (2 x + 1) + \frac{1}{4} cos (2 x + 1)

Add a constant to the solution

= \frac{1}{2} x sin (2 x + 1) + \frac{1}{4} cos (2 x + 1) + C

\int \frac{1}{x ^{2} + 2 x + 3} d x

\int \frac{x ^{3}}{( 1 + x ^{2} ) ^{2}} d x

\int \frac{x ^{5}}{1 + x ^{2}} d x

\int d (cos (x)) d x

\int \frac{1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

What is the integral of cos(2x+1)x ?
The integral of cos(2x+1)x is 1/2 xsin(2x+1)+1/4 cos(2x+1)+C