\lim_{x \rightarrow \infty}\frac{2x^2+3x-6}{x^3+8x^2+9x-100}

\lim_{x \rightarrow 0}\big(\frac{7x+8}{5x+4}\big)^{\frac{2}{x}}

\infty

\int_{}^{} \frac{dx}{3^2+x^2}

\frac{1}{3}arctg\frac{x}{3}+C

\int_0^1 \big(2x^2-2x-7\big)dx

-7\frac{1}{3}

\lim_{x \rightarrow \pi}\frac{sin\space x}{x}

\lim_{x \rightarrow -2}\big(1-3x^3+4x^4\big)

\lim_{x \rightarrow \infty}\big(\frac{2x+1}{x-2}\big)

\lim_{x \rightarrow \infty}\frac{5x^2-3x+2}{3x^2+x-9}

\frac{5}{3}

\int_{}^{} \frac{ln \space x}{x}dx

\frac{\big(ln \space x\big)^2}{2}+C

\lim_{x \rightarrow \infty}\big(\frac{x-2}{3x+1}\big)^{2x}