Math  /  Calculus

Question29. (x2x+1)dxx2+x\int \frac{\left(x^{2}-x+1\right) d x}{x^{2}+x}

Studdy Solution
Combine the results:
x2x+1x2+xdx=x+lnx3lnx+1+C\int \frac{x^2 - x + 1}{x^2 + x} \, dx = x + \ln |x| - 3 \ln |x + 1| + C
where CC is the constant of integration.
The antiderivative is:
x+lnx3lnx+1+C\boxed{x + \ln |x| - 3 \ln |x + 1| + C}

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