Find : $\large\textstyle\int\!{\large\frac{x^{2}+x+1}{(x^{2}+1)\left(x+2\right)}}\,d x.$

Find : $\large\textstyle\int(3x+1)\large{\sqrt{4-3x-2x^{2}}}d x\,.$

Evaluate : $\large\textstyle\int$$\large{\frac{x}{(x-1)^{2}(x+2)}}d x\ .$

Find : $\large\textstyle\int$$\large{\frac{x}{(x^{2}+1)(x-1)}}\,d x.$

Find : $\large\textstyle\int$$(x+3){\sqrt{3-4x-x^{2}}}\ d x\ .$

Evaluate : $\large\textstyle\int(x-3){\sqrt{x^{2}+3x-18}}\,d x\,.$

Evaluate : $\large\textstyle\int\!{\frac{x+2}{\sqrt{x^{2}+5x+6}}}d x~.$

Evaluate : $\large\textstyle\int\!{\frac{3x+1}{(x+1)^{2}(x+3)}}d x~.$

Evaluate : $\large\textstyle\int{\frac{3x+1}{(x^{3}-x^{2}-x+1)}}d x\,.$