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

The integral of sec^2(2x)sin(2x) is 1/2 cos(2x)+1/2 sin(2x)tan(2x)+C

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integral of sec^2(2x)sin(2x)

\int sec^{2} (2 x) sin (2 x) d x

\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

Solution steps

\int sec^{2} (2 x) sin (2 x) d x

Simplify

sec^{2} (2 x) sin (2 x) : sec (2 x) tan (2 x)

= \int sec (2 x) tan (2 x) d x

Rewrite using trig identities

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

Apply Integration By Parts

: - \int sin (2 x) d x + \frac{1}{2} sin (2 x) tan (2 x)

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

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

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

Simplify

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

Add a constant to the solution

= \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

x \to - \infty lim (g (x))

\int 13 sin^{6} (x) cos^{3} (x) d x

\int_{0}^{2} π (16 - y^{4}) d y

\frac{d}{d x} ((1 + \frac{10}{x})^{x})

cos (t) + t sin (t)

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