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

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

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

$$\mathrm{I}\mathrm{need}\mathrm{u}\mathrm{help}$$

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

$$\mathrm{Expand}{(x^m-x^n)}^2$$$$x^{2m}-2x^m{x}^n+x^{2n}$$$$\mathrm{Divide}\mathrm{by}\sqrt{x}\mathrm{and}\mathrm{integrate}$$

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

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

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