Ans:Hello Student,Please find answer to your question belowDo the long division, we have

Grade 12Integral Calculus

∫(x²+1)/(x+1) dx

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

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