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Question Number 95009 by bobhans last updated on 22/May/20

$$\int \frac{e^x+2{xe}^x\sin x-2{xe}^x\cos x}{\sqrt{x}\sin {}^{2}x}dx$$

Commented by bobhans last updated on 22/May/20

my children exam

Commented by  M±th+et+s last updated on 22/May/20

$$thinkthatits$$$$\int \frac{e^{x}sin\left(x\right)+2{xe}^{x}sin\left(x\right)-2{xe}^{x}cos\left(x\right)}{\sqrt{x}{sin}^2\left(x\right)}dx$$

Commented by bobhans last updated on 23/May/20

$$\mathrm{yes}.\mathrm{if}\int \frac{{\mathrm{e}}^{\mathrm{x}}\sin \left(\mathrm{x}\right)-{2\mathrm{xe}}^{\mathrm{x}}\sin \left(\mathrm{x}\right)-{2\mathrm{xe}}^{\mathrm{x}}\cos \left(\mathrm{x}\right)}{\sqrt{\mathrm{x}}\sin {}^2\left(\mathrm{x}\right)}\mathrm{dx}$$$$\mathrm{can}\mathrm{be}\mathrm{solved}.$$$$\int \frac{\mathrm{d}}{\mathrm{dx}}\left[\frac{2\sqrt{\mathrm{x}}{\mathrm{e}}^{\mathrm{x}}}{\sin \left(\mathrm{x}\right)}\right]=\frac{2\sqrt{\mathrm{x}}{\mathrm{e}}^{\mathrm{x}}}{\sin \left(\mathrm{x}\right)}+\mathrm{c}$$

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