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

The integral of sec^2(x)sqrt(tan(x)) is 2/3 tan^{3/2}(x)+C

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

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

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = tan (x)

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

Add a constant to the solution

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

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