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

The integral of cos^{-2}(2x) is 1/2 tan(2x)+C

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integral of cos^{-2}(2x)

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

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

Solution steps

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

Simplify

cos^{- 2} (2 x) : sec^{2} (2 x)

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

Apply u-substitution

: \int sec^{2} (u) \frac{1}{2} d u

= \int sec^{2} (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{2} tan (u)

Substitute back

u = 2 x

= \frac{1}{2} tan (2 x)

Add a constant to the solution

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

n = 0 \sum \infty \frac{1}{5 ^{n}}

x y^{^{'}} + 6 y = 3 x + 1

\frac{d}{d x} (1 - x^{6})

\int cos (x + 1) d x

\int_{- \infty}^{0} \frac{1}{7 - 6 x} d x

What is the integral of cos^{-2}(2x) ?
The integral of cos^{-2}(2x) is 1/2 tan(2x)+C