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Grade 12Integral Calculus

∫(x³-1)(x+2)/(x²+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

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

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