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

The integral of sec^2(2a)x is (x^2sec^2(2a))/2+C

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integral of sec^2(2a)x

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

\frac{x ^{2} sec ^{2} ( 2 a )}{2} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= sec^{2} (2 a) \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{2} sec ^{2} ( 2 a )}{2}

Add a constant to the solution

= \frac{x ^{2} sec ^{2} ( 2 a )}{2} + C

\frac{1}{u}

\frac{1}{t}

\int \frac{1}{- x ^{2} - 8 x} d x

\int \frac{d}{1} (x sin (x)) d x

\int \frac{x + 3}{x} d x

What is the integral of sec^2(2a)x ?
The integral of sec^2(2a)x is (x^2sec^2(2a))/2+C