What is the integral of sin(2x+pi) ?

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

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integral of sin(2x+pi)

\int sin (2 x + π) d x

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

Solution steps

\int sin (2 x + π) d x

Apply Integration By Parts

= x sin (2 x + π) - \int - 2 x cos (2 x) d x

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

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

Simplify

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

Add a constant to the solution

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

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