What is the integral of cos(3x-2pi)cos(x+pi) ?

The integral of cos(3x-2pi)cos(x+pi) is -cos(3x-2pi)sin(x)-3/2 (-1/4 sin(4x)+1/2 sin(2x))+C

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integral of cos(3x-2pi)cos(x+pi)

\int cos (3 x - 2 π) cos (x + π) d x

- cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

Solution steps

\int cos (3 x - 2 π) cos (x + π) d x

Apply Integration By Parts

: - cos (3 x - 2 π) sin (x) - \int 3 sin (3 x) sin (x) d x

= - cos (3 x - 2 π) sin (x) - \int 3 sin (3 x) sin (x) d x

\int 3 sin (3 x) sin (x) d x = \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x))

= - cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x))

Add a constant to the solution

= - cos (3 x - 2 π) sin (x) - \frac{3}{2} (- \frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

2 (x^{3} - x)^{4}

n = 2 \sum \infty \frac{2}{n ^{3}}

n = 0 \sum \infty 2^{2 n}

\frac{d}{d x} (a^{f (x)})

\int e^{- θ} cos (2 θ) d θ

What is the integral of cos(3x-2pi)cos(x+pi) ?
The integral of cos(3x-2pi)cos(x+pi) is -cos(3x-2pi)sin(x)-3/2 (-1/4 sin(4x)+1/2 sin(2x))+C