Compute <mrow> 4 t </mrow> <mrow> 5 <mroot> <mrow

Kiersten Hodge 2022-05-13 Answered
Compute 4 t 5 2 t + 3 3 d t.
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Answers (1)

Darion Sexton
Answered 2022-05-14 Author has 15 answers

Since 45 is constant with respect to t, move 45 out of the integral.

45t2t+33dt

Let u=2t+3. Then du=2dt, so 12du=dt. Rewrite using u and du.

45u2-32u312du

Simplify.

45u-34u3du

Since 14 is constant with respect to u, move 14 out of the integral.

45(14u-3u3du)

Simplify the expression.

15(u-3)u-13du

Expand (u-3)u-13.

15u23-3u-13du

Split the single integral into multiple integrals.

15(u23du+-3u-13du)

By the Power Rule, the integral of u23 with respect to u is 35u53.

15(35u53+C+-3u-13du)

Since -3 is constant with respect to u, move -3 out of the integral.

15(35u53+C-3u-13du)

By the Power Rule, the integral of u-13 with respect to u is 32u23.

15(35u53+C-3(32u23+C))

Simplify.

15(3u535-9u232)+C

Replace all occurrences of u with 2t+3.

15(3(2t+3)535-9(2t+3)232)+C

Simplify.

3(2t+3)23(4t-9)50+C

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