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Popular >

integral of sec^{11}(x)

Solution

\int sec^{11} (x) d x

Solution

\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣)))) + C

Solution steps

\int sec^{11} (x) d x

Apply Integral Reduction

= \frac{sec ^{10} ( x ) sin ( x )}{10} + \frac{9}{10} \cdot \int sec^{9} (x) d x

\int sec^{9} (x) d 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) ∣)))

= \frac{sec ^{10} ( x ) sin ( x )}{10} + \frac{9}{10} (\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) ∣))))

Simplify

\frac{sec ^{10} ( x ) sin ( x )}{10} + \frac{9}{10} (\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) ∣)))) : \frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))

= \frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))

Add a constant to the solution

= \frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣)))) + C

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Frequently Asked Questions (FAQ)

What is the integral of sec^{11}(x) ?
The integral of sec^{11}(x) is