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Int(x-1)(x-2)/x+4 dx ?

1 Answer

Apr 28, 2018

$I = \frac{1}{2} x^{2} - 7 x + 30 ln (| x + 4 |) + C$ $I=1/2x^2-7x+30ln(abs(x+4))+C$

Explanation:

I assume you meant

$I = \int \frac{(x - 1) (x - 2)}{x + 4} d x$ $I=int((x-1)(x-2))/(x+4)dx$

$I = \int \frac{x^{2} - 3 x + 2}{x + 4} d x$ $color(white)(I)=int(x^2-3x+2)/(x+4)dx$

By long division

$I = \int x - 7 + 30 \frac{1}{x + 4} d x$ $I=intx-7+30 1/(x+4)dx$

$I = \int x d x - \int 7 d x + 30 \int \frac{1}{x + 4} d x$ $color(white)(I)=intxdx-int7dx+30int1/(x+4)dx$

$I = \frac{1}{2} x^{2} - 7 x + 30 ln (| x + 4 |) + C$ $color(white)(I)=1/2x^2-7x+30ln(abs(x+4))+C$

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