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Q.

$\int \frac{dx}{(x - 2)^{7 / 8} (x + 3)^{9 / 8}} =$

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a

$\frac{8}{5} {(\frac{x - 2}{x + 3})}^{1 / 8} + c$

b

$\frac{8}{5} {(\frac{x + 2}{x + 3})}^{1 / 8} + c$

c

$\frac{4}{5} {(\frac{x - 2}{x + 3})}^{1 / 8} + c$

d

$\frac{5}{8} {(\frac{x - 2}{x + 3})}^{1 / 8} + c$

answer is A.

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Detailed Solution

$I = \int \frac{dx}{{(\frac{x - 2}{x + 3})}^{\frac{7}{8}} (x + 3)^{2}} Put \frac{x - 2}{x + 3} = t \Rightarrow \frac{5}{{(x + 3)}^{2}} dx = dt I = \frac{1}{5} \int \frac{dt}{{(t)}^{\frac{7}{8}}} = \frac{8}{5} t^{\frac{1}{8}} + c = \frac{8}{5} {(\frac{x - 2}{x + 3})}^{\frac{1}{8}} + c$

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