∫ x ^ 2 x ^ 2 +4 dx =∫ x ^ 2 +4 4 x ^ 2 +4 dx =∫ x ^ 2 +4 x ^ 2 +4 dx ∫ 4 x ^ 2 +4 dx =∫ dx 4∫ 1 x ^ 2 + 2 ^ 2 dx =x ...

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Algebra of Limits

Solve: ∫x2x2...

Question

Solve: $\int \frac{x^{2}}{x^{2} + 4} d x$

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Solution

$\int \frac{x^{2}}{x^{2} + 4} d x = \int \frac{x^{2} + 4 - 4}{x^{2} + 4} d x = \int \frac{x^{2} + 4}{x^{2} + 4} d x - \int \frac{4}{x^{2} + 4} d x = \int d x - 4 \int \frac{1}{x^{2} + 2^{2}} d x = x - 4 (\frac{1}{2} {tan}^{- 1} \frac{x}{2}) + C = x - 2 {tan}^{- 1} \frac{x}{2} + c$

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