Question

Rewriting Integrals before Integrating!

So I'm not very good with radicals, any tips or suggestions would be great!

Question: indefinite integral (1)/(x sq root (x) (dx)
I need to "rewrite" the indefinite integral before integrating!

Answer 1

\[x\sqrt{x} = x^{2/2}*x^{1/2} = x^{\frac{ 2 }{ 2 }+\frac{ 1 }{ 2 }} = x^{3/2}\]

Answer 2

\[\int\limits_{}^{}\frac{ 1 }{ x\sqrt{x} }dx = \int\limits_{}^{}\frac{ 1 }{ x^{3/2} }dx = \int\limits_{}^{}x^{-3/2}dx\]

This is likely what was wanted. As for tips, just remember some basic exponent rules. You can always combine multiplication of x's or roots of x as long as you know their exponential form and knowing that when you multiply exponents of the same base, you add the exponents, as I did above. Hope it makes sense :)

Answer 3

@Concentrationalizing thank you so much. Your first response helped alot! Now I know how they got the answer.