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∫(x 3 -1)(x+2)/(x 2 +x+1) dx

∫(x3-1)(x+2)/(x2+x+1) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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