Some Special Types of Integrals (Contd…)

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Example:

Evaluate the integral

Suggested answer:

Referring to the above procedure (ii), we have

Comparing the coefficients of x and

4A = 1 B = 1

B = 1

Put (2x² + 3) = t

Substituting I₁ and I₂ from (2) and (3) respectively in (1) we have

Integral of the form

Method:

Taking 1 as the second function and integrating by parts, we get

Integral of the form

Method:

We make the substitution

(1+t²)dx 2dt

Similarly,

By making the above substitutions the integrals will be reduced to the form  which can be integrated by method of completing squares.

Example:

Suggested answer:

dt = dZ