What is the integral of tan(x)sec^{5/2}(x) ?

The integral of tan(x)sec^{5/2}(x) is 2/5 sec^{5/2}(x)+C

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integral of tan(x)sec^{5/2}(x)

\int tan (x) sec^{\frac{5}{2}} (x) d x

\frac{2}{5} sec^{\frac{5}{2}} (x) + C

Solution steps

\int tan (x) sec^{\frac{5}{2}} (x) d x

Apply u-substitution

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

Apply the Power Rule

= \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = sec (x)

= \frac{2}{5} sec^{\frac{5}{2}} (x)

Add a constant to the solution

= \frac{2}{5} sec^{\frac{5}{2}} (x) + C

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What is the integral of tan(x)sec^{5/2}(x) ?
The integral of tan(x)sec^{5/2}(x) is 2/5 sec^{5/2}(x)+C