Methods of Integration

Methods of Integration

(a) Integration by substitution (or by change of independent variable)

It reduces the integral to either a standard form or makes it easier to integrate

Say

Let = cos θ then the integral reduces to

=

= - 4

= -2 = -2 sin θ + θ + sin θ cos θ + c

= -2

(b) Integration by parts

(Here u and v are function of x}

The choice of 'v' should be made by the thought that 'v' should be easily integrable. A heuristic approach to find 'u' & 'v' is through ILATE rule where

I stands for Inverse Circular function

L stands for Logarithmic function

A stands for Algebraic function

T stands for Trigonometric function

E stands for Exponential function

The integration is easier for the function which comes later in the above rule.