What is the integral of sec(2)(x)tan(2)(x) ?

The integral of sec(2)(x)tan(2)(x) is 1/3 sec(2)tan(2)x^3+C

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integral of sec(2)(x)tan(2)(x)

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

\frac{1}{3} sec (2) tan (2) x^{3} + C

Solution steps

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

Take the constant out:

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

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

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= sec (2) tan (2) \frac{x ^{3}}{3}

Simplify

sec (2) tan (2) \frac{x ^{3}}{3} : \frac{1}{3} sec (2) tan (2) x^{3}

= \frac{1}{3} sec (2) tan (2) x^{3}

Add a constant to the solution

= \frac{1}{3} sec (2) tan (2) x^{3} + C

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What is the integral of sec(2)(x)tan(2)(x) ?
The integral of sec(2)(x)tan(2)(x) is 1/3 sec(2)tan(2)x^3+C