Find : $\textstyle\int$${\frac{e^{x}(x-3)}{(x-1)^{3}}}d x\,.$

Find : $\textstyle\int$${\frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}}}\,.$

Find : $\textstyle\int$$\left({\frac{1-x}{1+x^{2}}}\right)^{2}e^{x}d x~.$

Find : $\textstyle\int$$\textstyle\left\{{\frac{\left(x+\sin^{2}x\right)\sec^{2}x}{1+x^{2}}}\right\}d x~.$

Find : $\textstyle\int e^{x}\,{\frac{\sqrt{1+\sin2x}}{1+\cos2\,x}}\,d x$.

Find : $\textstyle\int$$\frac{d x}{5-8\,x-x^{2}}$

Find : $\textstyle\int{\frac{d x}{x^{2}+4x+8}}$

Find : $\textstyle\int$${\sqrt{x^{2}-2x}}\ d x$

Find : $\textstyle\int$$\sqrt{2x-x^{2}\ d x}$

Find : $\textstyle\int$$\frac{1}{\sqrt{x^{2}-4\,x}}\,d x$

Find : $\textstyle\int$$\frac{x}{\sqrt{32-x^{2}}}\,d x$

Find : $\textstyle\int$$\frac{d x}{\sqrt{3-2\,x-x^{2}}}$