What is the integral of sin(5θ-pi) ?

The integral of sin(5θ-pi) is θsin(5θ-pi)+θsin(5θ)+1/5 cos(5θ)+C

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integral of sin(5θ-pi)

\int sin (5 θ - π) d θ

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

Solution steps

\int sin (5 θ - π) d θ

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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