Use an appropriate substitution and then a trigonometric substitution to

Tyra

Tyra

Answered question

2021-10-14

Use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.
x1xdx

Answer & Explanation

Benedict

Benedict

Skilled2021-10-15Added 108 answers

Step 1: Given that
x1xdx
Step 2: Solve
We have,
x1xdx=xx2dx
(x2x)dx
(x2x+(12)2(12)2)dx
=14(x12)2dx
Substitute, 2x−1 = t, such that, 2.dx=dt
121(2x1)2dx=1412t2dt
=14[t21t2+12sin1(t)]+C
=(2x+1)81(2x1)2+18sin1(2x1)+C
=2x18×2xx2+18sin1(2x+1)+C
=(4x2)xx2+sin1(2x1)8+C

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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