Evaluate 8 7 &#xFEFF; </mrow> x 2 </mrow> ln

Yasmine Larson

Yasmine Larson

Answered question

2022-05-12

Evaluate 8 7  x 2 ln ( x ) 2 d x.

Answer & Explanation

Taniya Wood

Taniya Wood

Beginner2022-05-13Added 19 answers

Rewrite as 8x2(2ln(x))7dx.

8x2(2ln(x))7dx

Since 827 is constant with respect to x, move 827 out of the integral.

827x2(ln(x))dx

Multiply 8 by 2.

167x2(ln(x))dx

Integrate by parts using the formula udv=uv-vdu, where u=ln(x) and dv=x2.

167(ln(x)(13x3)-13x31xdx)

Simplify.

167(ln(x)x33-x23dx)

Since 13 is constant with respect to x, move 13 out of the integral.

167(ln(x)x33-(13x2dx))

By the Power Rule, the integral of x2 with respect to x is 13x3.

167(ln(x)x33-13(13x3+C))

Simplify the answer.

167(13ln(x)x3-19x3)+C

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