\int \frac{dx}{cos^{2}\space 3x}

\frac{1}{3}tg3x+C

\lim_{x \rightarrow 2}\frac{3x+1}{x^{2}+1}

\lim_{x \rightarrow \infty}\frac{7x^{3}+6x^{2}-9}{x^{2}+2x-1}

\infty

\lim_{x \rightarrow \infty}\frac{5x-6}{3x+2}

\frac{5}{3}

\lim_{x \rightarrow 0}\frac{sin\space 3x}{x}

\int_{}^{} \frac{x^2}{x^2+1}dx

x-arctg \space x+C

\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}