What is the integral of cos^2(x)-1 ?

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

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integral of cos^2(x)-1

integral

cos^{2} (x) - 1

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

Solution steps

\int cos^{2} (x) - 1 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 cos^{2} (x) d x - \int 1 d x

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

\int 1 d x = x

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

Simplify

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) - x : - \frac{1}{2} x + \frac{1}{4} sin (2 x)

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

Add a constant to the solution

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

\frac{x}{x + 3}

e^{\frac{1}{2}} x^{2}

\frac{sin ( x )}{1 + sin ^{2} ( x )}

y = ∣ x - 1 ∣

2 x^{2} + 5

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