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# Evaluate the integral.$\displaystyle \int \tan x \sec^3 x dx$

## $$\frac{1}{3} \sec ^{3} x+C$$

#### Topics

Integration Techniques

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### Video Transcript

This problem is from Chapter seven section to problem number twenty one in the book Calculus Early Transcendental Sze eighth Edition by James Door Here we have a indefinite a roll of tangent times he can't cube. So here, let's re write it Seeking cute Becks as c can't squared of eggs Time seeking a Vicks and let's sleep Tangent avec says it is The reason for doing this is because if we grouped these last two terms here to suggest that we should try a new substitution, you equal See Kanna Becks So that do you is seeking a bucks tangent of X t X, which is exactly what we have in the end A gram. So after using this u substitution R interval simply becomes you square, Do you? Now we can use the power rule to evaluate this integral you cubed over three plus Don't forget our constant of integration seat. And now we could come back to our Are you substitution to replace you with seeking of X? So we have He can't keep the bugs over three plus he and there's our answer. Thank you

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#### Topics

Integration Techniques

Lectures

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