What is the integral of (3cos(θ))^2 ?

The integral of (3cos(θ))^2 is 9θcos^2(θ)+9(-1/2 θcos(2θ)+1/4 sin(2θ))+C

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integral of (3cos(θ))^2

\int (3 cos (θ))^{2} d θ

9 θ cos^{2} (θ) + 9 (- \frac{1}{2} θ cos (2 θ) + \frac{1}{4} sin (2 θ)) + C

Solution steps

\int (3 cos (θ))^{2} d θ

Apply Integration By Parts

: 9 θ cos^{2} (θ) - \int - 18 θ cos (θ) sin (θ) d θ

= 9 θ cos^{2} (θ) - \int - 18 θ cos (θ) sin (θ) d θ

\int - 18 θ cos (θ) sin (θ) d θ = - 9 (- \frac{1}{2} θ cos (2 θ) + \frac{1}{4} sin (2 θ))

= 9 θ cos^{2} (θ) - (- 9 (- \frac{1}{2} θ cos (2 θ) + \frac{1}{4} sin (2 θ)))

Simplify

= 9 θ cos^{2} (θ) + 9 (- \frac{1}{2} θ cos (2 θ) + \frac{1}{4} sin (2 θ))

Add a constant to the solution

= 9 θ cos^{2} (θ) + 9 (- \frac{1}{2} θ cos (2 θ) + \frac{1}{4} sin (2 θ)) + C

e^{8 t}

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\frac{1}{x}, 9

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\frac{d y}{d x} = \frac{( y - 1 )}{x ^{2}}

What is the integral of (3cos(θ))^2 ?
The integral of (3cos(θ))^2 is 9θcos^2(θ)+9(-1/2 θcos(2θ)+1/4 sin(2θ))+C