# Topics of Integral Calculus

Integration of tanx: The integration tanx is log|sec x|+C.

Integration of cotx: The integration cotx is log|sin x|+C.

Integration of secx: The integration secx is log|secx + tanx|+C.

Integration of cosecx: The integration cosecx is log|cosecx – cotx|+C.

Integration of 1/x: The integration of 1/x is ln|x|+C.

Integration of lnx: The integration of lnx is xln x -x+C.

Integration of 2x: The integration of 2x is 2x/ln2+C.

Integration of tan2x: The integration of tan2x is tan(x)-x+C.

Integration of (ax+b)/(cx+d): The integration of (ax+b)/(cx+d) is ax/c + (bc-ad)/c2 ln|cx+d|+C.

Integration of e3x: The integration of e3x is e3x/3+C.

Integration of 1/root(x): The integration of $\frac{1}{\sqrt{x}}$ is $2\sqrt{x}+C$.

Integration of Cube root x: The integration of $\sqrt[3]{x}$ is $\frac{3}{4} x \sqrt[3]{x}+C$

Integration of Square root x: The integration of $\sqrt{x}$ is $\frac{2}{3} x\sqrt{x}+C$

Integration of log(sinx): $\int_0^{\pi/2} \log(\sin x) \ dx =-\frac{\pi}{2}\log 2$

Integration of 1/(1+x2): The integration of 1/(1+x2) is tan-1x+C.

Integration of Root (a2-x2): The integration of $\sqrt{a^2-x^2}$ is $\frac{x}{2} \sqrt{a^2-x^2}$ $+\frac{a^2}{2}\sin^{-1} \frac{x}{a}+C$.

Integration of Root (a2+x2): The integration of $\sqrt{a^2+x^2}$ is $\frac{x}{2} \sqrt{a^2+x^2}$ $+\frac{a^2}{2}\log |x+\sqrt{a^2+x^2}|+C$.