<s>[INST] How to integrate $\int (x-1)\sqrt{x} \, \text{d}x$ How do I find this integral:
$$\int (x-1)\sqrt{x} \, \text{d} x$$
I thought to use use substitution, but am not sure what I should use as $u$. 
 [/INST] $$\int { \left( x-1 \right) \sqrt { x } dx } =\int { \left( { x }^{ \frac { 3 }{ 2 }  }-{ x }^{ \frac { 1 }{ 2 }  } \right) dx= } \int { { x }^{ \frac { 3 }{ 2 }  } } dx-\int { { x }^{ \frac { 1 }{ 2 }  } } dx=\\ =\frac { 2 }{ 5 } { x }^{ \frac { 5 }{ 2 }  }-\frac { 2 }{ 3 } x^{ \frac { 3 }{ 2 }  }+C$$
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