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

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

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integral of sec^{3/2}(x)tan(x)

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

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

Solution steps

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

Apply u-substitution

: \int u^{\frac{1}{2}} d u

= \int u^{\frac{1}{2}} d u

Apply the Power Rule

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

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

Substitute back

u = sec (x)

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

Add a constant to the solution

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

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