What's the integral of #int tan^5(x) dx#?
2 Answers
Explanation:
# =int sin^4x(cosx)^-5 sinx dx#
# =int (1-cos^2x)^2(cosx)^-5 sinx dx#
# =int (1-2cos^2x + cos^4x)(cosx)^-5 sinx dx#
# =int ((cosx)^-5 -2(cosx)^-3 +(cosx)^-1) sinx dx#
Now integrate by substitution with
Alternatively, one could use the reduction formula for
Another method : )
For the two first integral let's
So
We have
(Don't forget absolute value,
Substitute back