A) \[4{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C\]
B) \[-\frac{4}{3}{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C\]
C) \[4{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C\]
D) \[-\frac{4}{3}{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C\]
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{\frac{dx}{{{\left( x+1 \right)}^{3/4}}{{\left( x-2 \right)}^{5/4}}}}\] \[\int_{{}}^{{}}{\frac{dx}{{{\left( \frac{x+1}{x-2} \right)}^{3/4}}{{\left( x-2 \right)}^{2}}}}\]put\[\frac{x+1}{x-2}=E\] \[\frac{-3}{{{\left( x-2 \right)}^{2}}}=\frac{dt}{dx}\]
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