Compute 3 5 x 5 </mrow> ln &#x2061;<!-- ⁡ x

revistasbibxjm87

revistasbibxjm87

Answered question

2022-05-11

Compute 3 5 x 5 ln ( x ) 3 d x.

Answer & Explanation

Gillian Kelly

Gillian Kelly

Beginner2022-05-12Added 11 answers

Rewrite as 3x5(3ln(x))5dx.

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3x5(3ln(x))5dx

Since 335 is constant with respect to x, move 335 out of the integral.

335x5(ln(x))dx

Multiply 3 by 3.

95x5(ln(x))dx

Integrate by parts using the formula udv=uv-vdu, where u=ln(x) and dv=x5.

95(ln(x)(16x6)-16x61xdx)

Simplify.

95(ln(x)x66-x56dx)

Since 16 is constant with respect to x, move 16 out of the integral.

95(ln(x)x66-(16x5dx))

By the Power Rule, the integral of x5 with respect to x is 16x6.

95(ln(x)x66-16(16x6+C))

Simplify the answer.

95(16ln(x)x6-136x6)+C

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