What is the integral of tan^n(x ?

The integral of tan^n(x is (x^2tan^n(d))/2+C

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integral of tan^n(x

\int tan^{n} (d) x d x

\frac{x ^{2} tan ^{n} ( d )}{2} + C

Solution steps

\int tan^{n} (d) x d x

Take the constant out:

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

= tan^{n} (d) \cdot \int x d x

Apply the Power Rule

= tan^{n} (d) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{x ^{2} tan ^{n} ( d )}{2}

Add a constant to the solution

= \frac{x ^{2} tan ^{n} ( d )}{2} + C