# Indefinite Integration

## Integration By Substitution – Formula and Examples

Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If $$\phi(x)$$ is continuously differentiable function, then to evaluate integrals of the form $$\int$$ …

## Integration Examples

Here you will learn some integration examples for better understanding of integration concepts. Example 1 : Evaluate : $$\int$$ $$dx\over {3sinx + 4cosx}$$ Solution : I = $$\int$$ $$dx\over {3sinx + 4cosx}$$ = $$\int$$ $$dx\over {3[{2tan{x\over 2}\over {1+tan^2{x\over 2}}}] + 4[{1-tan^2{x\over 2}\over {1+tan^2{x\over 2}}}]}$$ = $$\int$$ $$sec^2{x\over 2}dx\over {4+6tan{x\over 2}-4tan^2{x\over 2}}$$ let $$tan{x\over 2}$$ = …

## Integration of Tan Inverse x

Here you will learn proof of integration of tan inverse x or arctan x and examples based on it. Let’s begin – Integration of Tan Inverse x The integration of tan inverse x or arctan x is $$xtan^{-1}x$$ – $$1\over 2$$ $$log |1 + x^2|$$ + C Where C is the integration constant. i.e. $$\int$$ …

## Integration of Cos Inverse x

Here you will learn proof of integration of cos inverse x or arccos x and examples based on it. Let’s begin – Integration of Cos Inverse x The integration of cos inverse x or arccos x is $$xcos^{-1}x$$ – $$\sqrt{1 – x^2}$$ + C Where C is the integration constant. i.e. $$\int$$ $$cos^{-1}x$$ = $$xcos^{-1}x$$ …

## Integration of Sin Inverse x

Here you will learn proof of integration of sin inverse x or arcsin x and examples based on it. Let’s begin – Integration of Sin Inverse x The integration of sin inverse x or arcsin x is $$xsin^{-1}x$$ + $$\sqrt{1 – x^2}$$ + C Where C is the integration constant. i.e. $$\int$$ $$sin^{-1}x$$ = $$xsin^{-1}x$$ …

## What is the Integration of Log x dx ?

Here you will learn what is the integration of log x dx with respect to x and examples based on it. Let’s begin – Integration of Log x The integration of log x with respect to x is x(log x) – x + C. where C is the integration Constant. i.e. $$\int$$ log x dx …

## Integration of Cosecx

Here you will learn proof of integration of cosecx or cosec x and examples based on it. Let’s begin – Integration of Cosecx or Cosec x The integration of cosec x is log |cosec x – cot x| + C or $$log |tan {x\over 2}|$$ + C. where C is the integration constant. i.e. $$\int$$ …

## Integration of Secx

Here you will learn proof of integration of secx or sec x and examples based on it. Let’s begin – Integration of Secx or Sec x The integration of sec x is log |sec x + tan x| + C or $$log |tan ({\pi\over 4} + {x\over 2})|$$ + C. where C is the integration constant. …