Compute 2 3 t 2 </mrow> sec 2 </mro

Jordon Haley

Jordon Haley

Answered question

2022-05-11

Compute 2 3 t 2 sec 2 ( 3 t 3 + 1 ) d t.

Answer & Explanation

Mackenzie Zimmerman

Mackenzie Zimmerman

Beginner2022-05-12Added 15 answers

Simplify.

2t2sec2(3t3+1)3dt

Since 23 is constant with respect to t, move 23 out of the integral.

23t2sec2(3t3+1)dt

Let u=3t3+1. Then du=9t2dt, so 19du=t2dt. Rewrite using u and du.

23sec2(u)19du

Combine sec2(u) and 19.

23sec2(u)9du

Since 19 is constant with respect to u, move 19 out of the integral.

23(19sec2(u)du)

Simplify.

227sec2(u)du

Since the derivative of tan(u) is sec2(u), the integral of sec2(u) is tan(u).

227(tan(u)+C)

Simplify.

227tan(u)+C

Replace all occurrences of u with 3t3+1.

227tan(3t3+1)+C

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