Math Challenges

Submissions for Problem #34

Find the general antiderivative.

\[ \int_{}^{}\sec^6\left(x\right)dx \]

zapwai

Solution: \( \displaylines{\int\sec^6x=\int\sec^2x\sec^4x=\int\sec^2x\left(1+\tan^2x\right)^2\\ \int\sec^2x\left(\tan^4x+2\tan^2x+1\right)\\ =\frac15\tan^5x+\frac23\tan^3x+\tan x+C\\ } \)

Explanation:
The second to third line is done with a u-substitution, u = tan(x)