Compute 3 4 &#xFEFF; </mrow> x 3 </mrow> ln

Autumn Pham

Autumn Pham

Answered question

2022-05-12

Compute 3 4  x 3 ln ( 3 x ) d x.

Answer & Explanation

stafninumfu1tf

stafninumfu1tf

Beginner2022-05-13Added 18 answers

Simplify.

3x3ln(3x)4dx

Since 34 is constant with respect to x, move 34 out of the integral.

34x3ln(3x)dx

Integrate by parts using the formula udv=uv-vdu, where u=ln(3x) and dv=x3.

34(ln(3x)(14x4)-14x4(-12x)dx)

Simplify.

34(ln(3x)x44--x38dx)

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

34(ln(3x)x44--x38dx)

Simplify.

34(ln(3x)x44+x38dx)

Since 18 is constant with respect to x, move 18 out of the integral.

34(ln(3x)x44+18x3dx)

By the Power Rule, the integral of x3 with respect to x is 14x4.

34(ln(3x)x44+18(14x4+C))

Simplify the answer.

34(14ln(3xx)x4+132x4)+C

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