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

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

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integral of (sin^2(2x))/(cos^2(x))

integral

\frac{sin ^{2} ( 2 x )}{cos ^{2} ( x )}

2 x - sin (2 x) + C

Solution steps

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

Rewrite using trig identities

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Rewrite using trig identities

= 4 \cdot \int \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \frac{1}{2} \cdot \int 1 - cos (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

= 4 \cdot \frac{1}{2} (\int 1 d x - \int cos (2 x) d x)

\int 1 d x = x

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

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

Simplify

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

= 2 x - sin (2 x)

Add a constant to the solution

= 2 x - sin (2 x) + C

e^{\frac{- x ^{2}}{3}}

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

(1 + t^{2})^{- 1}

\frac{( 7 ^{x} - 1 )}{x}

\frac{x}{4 + x}

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