Problem

a) arctgx1+x2dx

Answer

Expert–verified
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Answer

Substitute arctgx back as y: 12ln(1+x2)+C

Steps

Step 1 :Let y=arctgx

Step 2 :Differentiate with respect to x: dydx=11+x2

Step 3 :Substitute y back into the integral: ydy=12y2+C

Step 4 :Substitute arctgx back as y: 12ln(1+x2)+C

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