What is the integral of \sqrt[7]{tan(2x)}sec^2(2x) ?

The integral of \sqrt[7]{tan(2x)}sec^2(2x) is 7/16 tan^{8/7}(2x)+C

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integral of \sqrt[7]{tan(2x)}sec^2(2x)

\frac{7}{16} tan^{\frac{8}{7}} (2 x) + C

Solution steps

Apply u-substitution

: \int \frac{7 u ^{7}}{2} d u

= \int \frac{7 u ^{7}}{2} d u

Take the constant out:

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

= \frac{7}{2} \cdot \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{7}{2} \cdot \frac{u ^{8}}{8}

Substitute back

Simplify

= \frac{7}{16} tan^{\frac{8}{7}} (2 x)

Add a constant to the solution

= \frac{7}{16} tan^{\frac{8}{7}} (2 x) + C

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What is the integral of \sqrt[7]{tan(2x)}sec^2(2x) ?
The integral of \sqrt[7]{tan(2x)}sec^2(2x) is 7/16 tan^{8/7}(2x)+C