<s>[INST] Calculate:$\int \frac{1}{(x+1)^\frac{3}{4}(x+2)^{\frac{5}{4}}}\ dx$ Calculate following integration
$$\int \frac{1}{(x+1)^\frac{3}{4}(x+2)^{\frac{5}{4}}}\ dx$$ 
 [/INST] $\dfrac{1}{(x+1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}=\dfrac{1}{(x+1)^{2}(\dfrac{x+2}{x+1})^{\frac{5}{4}}}=\dfrac{1}{(x+1)^{2}(1+\dfrac{1}{x+1})^{\frac{5}{4}}}$ So, make a $\dfrac{1}{x+1}$ substitution and we get the answer.
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