∫x^2 1x^2 + 1 dx = ∫x^2 + 1 2x^2 + 1 dx = ∫(1 2x^2 + 1)dx = x 2tan^ 1 x + c #160; (Ans) ...

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Monotonically Increasing Functions

Evaluate ∫x...

Question

Evaluate $\int \frac{x^{2} - 1}{x^{2} + 1} d x$

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Solution

$\int \frac{x^{2} - 1}{x^{2} + 1} d x$

$= \int \frac{x^{2} + 1 - 2}{x^{2} + 1} d x$

$= \int (1 - \frac{2}{x^{2} + 1}) d x$

$= x - 2 {tan}^{- 1} x + c$ (Ans)

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