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

The integral of tan^{5/2}(x)sec^2(x) is 2/7 tan^{7/2}(x)+C

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

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

\frac{2}{7} tan^{\frac{7}{2}} (x) + C

Solution steps

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

Apply u-substitution

: \int u^{\frac{5}{2}} d u

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

Apply the Power Rule

: \frac{2}{7} u^{\frac{7}{2}}

= \frac{2}{7} u^{\frac{7}{2}}

Substitute back

u = tan (x)

= \frac{2}{7} tan^{\frac{7}{2}} (x)

Add a constant to the solution

= \frac{2}{7} tan^{\frac{7}{2}} (x) + C

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What is the integral of tan^{5/2}(x)sec^2(x) ?
The integral of tan^{5/2}(x)sec^2(x) is 2/7 tan^{7/2}(x)+C