Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{x^2+3x-1}{(x+1)^2}dx$
$I = \int \frac{x^2+x+2x-1}{(x+1)^2}dx$
$I = \int \frac{x^2+x+2x+2-3}{(x+1)^2}dx$
$I = \int [x+\frac{1}{x+1}-\frac{3}{(x+1)^2}]dx$
$I = \int xdx+\int \frac{1}{x+1}dx-\int \frac{3}{(x+1)^2}dx$
$I = \frac{x^2}{2}+\int \frac{1}{x+1}dx-\int \frac{3}{(x+1)^2}dx$
$I = \frac{x^2}{2}+log(x+1)-\int \frac{3}{(x+1)^2}dx$
$I = \frac{x^2}{2}+log(x+1)+\frac{3}{x+1}+c$