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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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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