What is the integral of 4cos^2(x)-2sin^2(x) ?

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

integral of 4cos^2(x)-2sin^2(x)

integral

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

x + \frac{3}{2} sin (2 x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= 2 x + sin (2 x) - (x - \frac{1}{2} sin (2 x))

Simplify

2 x + sin (2 x) - (x - \frac{1}{2} sin (2 x)) : x + \frac{3}{2} sin (2 x)

= x + \frac{3}{2} sin (2 x)

Add a constant to the solution

= x + \frac{3}{2} sin (2 x) + C

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in t e g r a l a^{12} y^{4} - a^{4} y^{12}

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