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Micah Haynes

Micah Haynes

Answered question

2022-04-04

What is ( 3 t 4 t + 2 )  d t?

Answer & Explanation

Ariella Bruce

Ariella Bruce

Beginner2022-04-05Added 19 answers

Remove parentheses.

-3t4-t+2dt

Split the single integral into multiple integrals.

-3t4dt+-tdt+2dt

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

-3t4dt+-tdt+2dt

By the Power Rule, the integral of t4 with respect to t is 15t5.

-3(15t5+C)+-tdt+2dt

Since -1 is constant with respect to t, move -1 out of the integral.

-3(15t5+C)-tdt+2dt

By the Power Rule, the integral of t with respect to t is 12t2.

-3(15t5+C)-(12t2+C)+2dt

Apply the constant rule.

-3(15t5+C)-(12t2+C)+2t+C

Simplify.

-3t55-t22+2t+C

Reorder terms.

-35t5-12t2+2t+C

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