What is the integral of sin(5x-pi) ?

The integral of sin(5x-pi) is xsin(5x-pi)+xsin(5x)+1/5 cos(5x)+C

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integral of sin(5x-pi)

\int sin (5 x - π) d x

x sin (5 x - π) + x sin (5 x) + \frac{1}{5} cos (5 x) + C

Solution steps

\int sin (5 x - π) d x

Apply Integration By Parts

: x sin (5 x - π) - \int - 5 x cos (5 x) d x

= x sin (5 x - π) - \int - 5 x cos (5 x) d x

\int - 5 x cos (5 x) d x = - x sin (5 x) - \frac{1}{5} cos (5 x)

= x sin (5 x - π) - (- x sin (5 x) - \frac{1}{5} cos (5 x))

Simplify

= x sin (5 x - π) + x sin (5 x) + \frac{1}{5} cos (5 x)

Add a constant to the solution

= x sin (5 x - π) + x sin (5 x) + \frac{1}{5} cos (5 x) + C

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\int (x sec^{2} (x)) d x

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What is the integral of sin(5x-pi) ?
The integral of sin(5x-pi) is xsin(5x-pi)+xsin(5x)+1/5 cos(5x)+C