∫(x^2+2)dxx+1=∫x^2 1+3x+1dx = ∫ [ (x 1)(x+1)(x+1)+3x+1 ]dx =∫ (x 1)dx+∫3x+1dx =x^22 x+3log| x+1|+c nbsp; where c is constant of integration Hence, the re ...

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Standard IX

Mathematics

Property 3

Evaluate: ∫x2...

Question

Evaluate: $\int \frac{(x^{2} + 2) d x}{x + 1}$

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Solution

$\int \frac{(x^{2} + 2) d x}{x + 1} = \int \frac{x^{2} - 1 + 3}{x + 1} d x$

$= \int [\frac{(x - 1) (x + 1)}{(x + 1)} + \frac{3}{x + 1}] d x$

$= \int (x - 1) d x + \int \frac{3}{x + 1} d x$

$= \frac{x^{2}}{2} - x + 3 log ∣ x + 1 ∣ + c$

where $c$ is constant of integration
Hence, the required integration is $= \frac{x^{2}}{2} - x + 3 log ∣ x + 1 ∣ + c$ .

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Property 3

Standard IX Mathematics

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Evaluate: ∫(x2+2)dxx+1

∫(x2+2)dxx+1=∫x2−1+3x+1dx =∫[(x−1)(x+1)(x+1)+3x+1]dx =∫(x−1)dx+∫3x+1dx =x22−x+3log∣x+1∣+c where c is constant of integration Hence, the required integration is =x22−x+3log∣x+1∣+c .

Evaluate: $\int \frac{(x^{2} + 2) d x}{x + 1}$