What is the integral of (2cos(x))^2 ?

The integral of (2cos(x))^2 is 4xcos^2(x)-2xcos(2x)+sin(2x)+C

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integral of (2cos(x))^2

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

4 x cos^{2} (x) - 2 x cos (2 x) + sin (2 x) + C

Solution steps

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

Apply Integration By Parts

: 4 x cos^{2} (x) - \int - 4 x sin (2 x) d x

= 4 x cos^{2} (x) - \int - 4 x sin (2 x) d x

\int - 4 x sin (2 x) d x = 2 x cos (2 x) - sin (2 x)

= 4 x cos^{2} (x) - (2 x cos (2 x) - sin (2 x))

Simplify

= 4 x cos^{2} (x) - 2 x cos (2 x) + sin (2 x)

Add a constant to the solution

= 4 x cos^{2} (x) - 2 x cos (2 x) + sin (2 x) + C

\frac{\partial}{\partial y} (5)

f (x) = - x^{2} + x, (- 1, - 2)

\int (x - 4)^{2} d x

y^{^{''}} + 4 y^{^{'}} = 17 cos (t), y (0) = - 1, y^{^{'}} (0) = 0

\frac{d}{d x} (- \frac{16}{( 1 + 4 x ) ^{2}})

What is the integral of (2cos(x))^2 ?
The integral of (2cos(x))^2 is 4xcos^2(x)-2xcos(2x)+sin(2x)+C