Question

Evaluate the integral. (Remember to use absolute values where appropriate.) ? t sec^2 8t dt t/8 tan(8t) - 1/48 ln|sec(8t)| + C

          Evaluate the integral. (Remember to use absolute values where appropriate.)
? t sec^2 8t dt

t/8 tan(8t) - 1/48 ln|sec(8t)| + C

Added by Virginia H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/06/2024

Step 1

We have: $$\int t \sec^2(8t) dt$$ Let's use substitution method. Let $u = 8t$, then $\frac{du}{dt} = 8$, and $dt = \frac{1}{8} du$. Also, $t = \frac{u}{8}$. Now, substitute these values into the integral: $$\int \frac{u}{8} \sec^2(u) \frac{1}{8} du$$ Simplify Show more…

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