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∫(x 2 +1)/(x+1) dx

∫(x2+1)/(x+1) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{x^2+1}{x+1}dx
Do the long division, we have
I = \int (x+\frac{2}{x+1}-1)dx
I = \int xdx+\int \frac{2}{x+1}dx-\int dx
I = \frac{x^2}{2}+\int \frac{2}{x+1}dx-\int dx
I = \frac{x^2}{2}+2log(x+1)-\int dx
I = \frac{x^2}{2}+2log(x+1)-x+c

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