x-m-x-n-2-x-dx-

Question Number 101286 by student work last updated on 01/Jul/20

\int \frac{{(x^{m} - x^{n})}^{2}}{\sqrt{x}} dx = ?

Commented by student work last updated on 01/Jul/20

I need u help

Commented by prakash jain last updated on 01/Jul/20

Expand {(x^{m} - x^{n})}^{2}

x^{2 m} - 2 x^{m} x^{n} + x^{2 n}

Divide by \sqrt{x} and integrate

Commented by Dwaipayan Shikari last updated on 02/Jul/20

\int \frac{x^{2 m} - 2 x^{m + n} + x^{2 n}}{\sqrt{x}} = \int x^{2 m - \frac{1}{2}} - 2 x^{m + n - \frac{1}{2}} + x^{2 n - \frac{1}{2}}

\frac{x^{2 m + \frac{1}{2}}}{2 m + \frac{1}{2}} - \frac{2 x^{m + n + \frac{1}{2}}}{m + n + \frac{1}{2}} + \frac{x^{2 n + \frac{1}{2}}}{2 n + \frac{1}{2}} + C