An Integral

âˆ«x²+x-1x³+x² -6xdx

1 Answers

I = \int \frac{x^2+x-1}{x^3+x^2-6x} dx= \int \frac{x^2+x-1}{x(x^2+x-6)}dx = \int \frac{x^2+x-6+5}{x(x^2+x-6)}dx

\Rightarrow \int \frac{1}{x}\; dx + \int \frac{5}{x(x^2+x-6)} \; dx = \int \frac{1}{x}\; dx+\frac 56 \int \frac{x+1}{x^2+x-6} dx- \int \frac 5 {6x}dx

Which you can calculate.

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