Topics of Integral Calculus

Topics of Integral Calculus

• Integration: Definition, Properties, and Formulas
• Integration by Substitution Method

More Integration Problems:

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 2^x: The integration of 2^x is 2^x/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 1/root(x): The integration of $\frac{1}{\sqrt{x}}$ is 2√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 √x is $\frac{2}{3}$ x√x+C.

Integration of log(sinx): ∫$_0^{\pi/2}$ log(sin x)dx = $-\frac{\pi}{2}$ log 2.

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

More Integrals

Trigonometric Functions:

∫sin3x dx	∫sinx cosx dx	∫√(1+sin2x) dx
∫sin2x dx

Exponential & Logarithmic Functions:

	∫e2x dx	∫e3x dx
∫ e$^{x^2}$ dx

Algebraic Functions:

∫x1/4 dx	∫x/(1+x) dx	∫x/(1+x2) dx
	∫ xn dx	∫ √(a2-x2) dx
		∫ √(a2+x2) dx
		∫(√x +1/√x)dx