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Integral Calculus> integrate the following integral ∫ (x^2 +...

question mark

integrate the following integral
∫ (x^2 + 5x + 2)/x + 2 dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 Years ago

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

$I = \int \frac{x^2+5x+2}{x+2}dx$
$I = \int \frac{x^2+2x+3x+2}{x+2}dx$
$I = \int \frac{x^2+2x+3x+6-4}{x+2}dx$
$I = \int \frac{x(x+2)+3(x+2)-4}{x+2}dx$
$I = \int [x+3-\frac{4}{x+2}]dx$
$I = \int xdx+3\int dx-\int \frac{4}{x+2}dx$
$I = \frac{x^2}{2}+3\int dx-\int \frac{4}{x+2}dx$
$I = \frac{x^2}{2}+3x-\int \frac{4}{x+2}dx$
$I = \frac{x^2}{2}+3x-4log(x+2)+c$

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