\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}

\int_{\pi/2}^{3\pi/4} \frac{2}{sin^2x}dx

\int_{}^{} \frac{5dx}{sin^2x}

-5ctg \space x+c

\lim_{x \rightarrow -\infty}\big(\frac{x+7}{2x-6}\big)^{5x+1}

\infty

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

ln \sqrt{|2x+1|}+C