• Calculus
• OFFERED PRICE: Rs. 1,696
• View Details

Indirect Substitution



If the integrand is of the form f(x)g(x), where g(x) is a function of the integral of f(x), then put integral of f(x) = t.

 

Example -8: Evaluate 

Solution:       Integral of the numerator = x3/2 / 3/2

Put x3/2 = t.

We get I = 2/3 ∫dt/√t2 + a3

= 2/3 In |x3/2 + √x3 + a3| + c.



Derived Substitution

Some time it is useful to write the integral as a sum of two related integrals which can be evaluated by making suitable substitutions.

Examples of such integrals are: 

A. Algebraic Twins 



B. Trigonometric twins



Method of evaluating these integral are illustrated by mean of the following examples:

Example -9: Evaluate ∫ 5/ 1+ x4 dx.



For I2 , we write x + 1/x t = => (1 – 1/x2 )dx = dt

                       

Combining the two integrals, we get

                        

Example -10: Evaluate ∫√tanx dx.

Solution:       Put tanx = t2 => sec2x dx = 2t dt

                        => dx = 2tdt / 1 + t4



This can be solved by the method used in example (9).

To read more, Buy study materials of Indefinite integral comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900


• View Details Xpress Buy

Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution