Integrals · Class 12 · CBSE · Science Mathematics

Find ∫ x²/(x² + 1) dx.

Practice question from Integrals (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · Subjective · Q-48214D

Answer: Since x²/(x²+1) = 1 − 1/(x²+1), we get ∫ x²/(x²+1) dx = ∫[1 − 1/(x²+1)] dx = x − tan⁻¹x + C.

Solution

Rewrite the integrand as $\frac{x^2}{x^2+1}=1-\frac{1}{x^2+1}$ . Hence, $\int\frac{x^2}{x^2+1}\,dx=x-\tan^{-1}x+C$ .

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