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Evaluating Integrals (III)

shamieh

Active member
Sep 13, 2013
539
Evaluate the Integral.

Just need someone to check my work.
\(\displaystyle
\int sec^4y \, tan^4y\)

\(\displaystyle \tan^4y * sec^2y * sec^2y \, dx\)

\(\displaystyle tan^4y * (1 + tan^2y) * sec^2y\)

\(\displaystyle u = tany\)
\(\displaystyle du = sec^2y\)

\(\displaystyle \int u^4 * (1 + u^2) * du\)

\(\displaystyle \int u^4 + u^6 * du\)

\(\displaystyle \frac{u^5}{5} + \frac{u^7}{7} + C\)

\(\displaystyle \frac{tan^5x}{5} + \frac{tan^7x}{7} + C\)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Looks good to me :D