\(\displaystyle \int \dfrac{5}{x}\,dx\)

\(5\ln(\lvert x \rvert) + C\)

\(\displaystyle \int \dfrac{1}{4 - 3x}\,dx\)

\(\dfrac{-1}{3} + \ln(\lvert 4 - 3x \rvert) + C\)

\(\displaystyle \int \dfrac{\sec^2(3x)}{\tan(3x)}\,dx\)

\(\dfrac{1}{3} + \ln[\lvert \tan(3x) \rvert] + C\)

\(\displaystyle \int \dfrac{5}{3 - 2x}\,dx\)

\(\dfrac{-5}{2} + \ln(\lvert 3 - 2x \rvert) + C\)

\(\displaystyle \int \dfrac{x}{3x^2 + 1}\,dx\)

\(\dfrac{1}{6} + \ln\left(\left\lvert 3x^2 + 1 \right\rvert\right) + C\)

\(\displaystyle \int \dfrac{3}{3x - 5}\,dx\)

\(\ln\lvert 3x - 5 \rvert + C\)

\(\displaystyle \int \dfrac{2x^3 + 3x}{x^4 + 3x^2}\,dx\)

\(\dfrac{1}{2}\ln\left\lvert x^4 + 3x^2\right\rvert + C\)

\(\displaystyle \int \dfrac{3x^2 + x - 1}{x + 2}\,dx\)

\(\dfrac{3x^2}{2} - 5x + 9\ln\lvert x + 2 \rvert + C\)

\(\displaystyle \int \dfrac{x^2 - 3x}{x^3 - 3x^2}\,dx\)

\(\dfrac{1}{3}\ln\left\lvert x^3 - 3x^2 \right\rvert + C\)

\(\displaystyle \int \dfrac{1}{2x\ln(x)^4}\,dx\)

\(\dfrac{1}{8}\ln\left\lvert \ln x^4 \right\rvert + C\)

\(\displaystyle \int \dfrac{\sqrt{x}}{\sqrt{x} + 2}\,dx\)

\(x - 4\sqrt{x} + 8\ln\left\lvert \sqrt{x} + 2 \right\rvert + C\)

\(\displaystyle \int \dfrac{2x^2 + 7x - 3}{x - 2}\,dx\)

\(x^2 + 11x + 19\ln\lvert x - 2 \rvert + C\)

\(\displaystyle \int \dfrac{1}{2x}\,dx\)

\(\dfrac{1}{2}\ln\lvert 2x \rvert + C\)

\(\displaystyle \int \dfrac{xe^{x^2}}{5 - 3e^{x^2}}\,dx\)

\(\dfrac{-1}{6}\ln\left\lvert 5 - 3e^{x^2} \right\rvert + C\)

\(\displaystyle \int \tan x\,dx\)

\(-\ln\lvert \cos x \rvert + C\)