Integrate 3 4 &#xFEFF; </mrow> t 4 </mrow> ln &

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jistefaftexia99kq6

Answered question

2022-04-10

Integrate 3 4  t 4 ln ( t ) 3 with respect to t.

Answer & Explanation

Gillian Kelly

Gillian Kelly

Beginner2022-04-11Added 11 answers

Rewrite as 3t4(3ln(t))4dt.

3t4(3ln(t))4dt

Since 334 is constant with respect to t, move 334 out of the integral.

334t4(ln(t))dt

Multiply 3 by 3.

94t4(ln(t))dt

Integrate by parts using the formula udv=uv-vdu, where u=ln(t) and dv=t4.

94(ln(t)(15t5)-15t51tdt)

Simplify.

94(ln(t)t55-t45dt)

Since 15 is constant with respect to t, move 15 out of the integral.

94(ln(t)t55-(15t4dt))

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

94(ln(t)t55-15(15t5+C))

Simplify the answer.

94(15ln(t)t5-125t5)+C

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