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Popular >

integral of sec^9(x)

Solution

\int sec^{9} (x) d x

Solution

\frac{sec ^{8} ( x ) sin ( x )}{8} + \frac{7}{8} (\frac{1}{6} sec^{6} (x) sin (x) + \frac{5}{48} (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))) + C

Solution steps

\int sec^{9} (x) d x

Apply Integral Reduction

= \frac{sec ^{8} ( x ) sin ( x )}{8} + \frac{7}{8} \cdot \int sec^{7} (x) d x

\int sec^{7} (x) d x = \frac{1}{6} sec^{6} (x) sin (x) + \frac{5}{48} (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))

= \frac{sec ^{8} ( x ) sin ( x )}{8} + \frac{7}{8} (\frac{1}{6} sec^{6} (x) sin (x) + \frac{5}{48} (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣)))

Add a constant to the solution

= \frac{sec ^{8} ( x ) sin ( x )}{8} + \frac{7}{8} (\frac{1}{6} sec^{6} (x) sin (x) + \frac{5}{48} (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))) + C

Popular Examples

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\int \frac{3}{6 + 3 x} d x

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\int \frac{2}{nπ} sin (\frac{nπ x}{2}) d x

Frequently Asked Questions (FAQ)

What is the integral of sec^9(x) ?
The integral of sec^9(x) is