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**galactus** For #1, you can use parts. $\displaystyle \int[xcos^{2}(x)]dx$

Let $\displaystyle u=x, \;\ dv=cos^{2}(x)dx, \;\ du=dx$$\displaystyle , \;\ v=\int[cos^{2}(x)]dx=\frac{xsin(x)cos(x)}{2}+\frac{x^{2}}{2}=\frac{x sin(2x)+2x^{2}}{4}$

For #2: $\displaystyle \int[x^{2}\sqrt{2x^{3}}]dx$

Let $\displaystyle u=2x^{3}, \;\ du=6x^{2}dx, \;\ \frac{1}{6}du=x^{2}dx$

For #3: $\displaystyle \int[x^{2}\sqrt{2x^{3}-5}]dx$

Same substitutions as above, except use $\displaystyle u=2x^{3}-5$