Integrate 1 4 &#xFEFF; </mrow> x 5 </mrow> ln &

Jazlyn Raymond

Jazlyn Raymond

Answered question

2022-05-12

Integrate 1 4  x 5 ln ( x ) 2 with respect to x.

Answer & Explanation

Lucille Lucas

Lucille Lucas

Beginner2022-05-13Added 16 answers

Rewrite as x5(2ln(x))4dx.

x5(2ln(x))4dx

Since 24 is constant with respect to x, move 24 out of the integral.

24x5(ln(x))dx

Cancel the common factor of 2 and 4.

12x5(ln(x))dx

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

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

Simplify.

12(ln(x)x66-x56dx)

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

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

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

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

Simplify the answer.

12(16ln(x)x6-136x6)+C

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