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integrate the following integral ∫ (x^2 + 3x -1)?(x+1)^2 dx

 
integrate the following integral
∫ (x^2 + 3x -1)?(x+1)^2 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+3x-1}{(x+1)^2}dx
I = \int \frac{x^2+x+2x-1}{(x+1)^2}dx
I = \int \frac{x^2+x+2x+2-3}{(x+1)^2}dx
I = \int [x+\frac{1}{x+1}-\frac{3}{(x+1)^2}]dx
I = \int xdx+\int \frac{1}{x+1}dx-\int \frac{3}{(x+1)^2}dx
I = \frac{x^2}{2}+\int \frac{1}{x+1}dx-\int \frac{3}{(x+1)^2}dx
I = \frac{x^2}{2}+log(x+1)-\int \frac{3}{(x+1)^2}dx
I = \frac{x^2}{2}+log(x+1)+\frac{3}{x+1}+c

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