Integration by Substitution

Integration by Substitution

Integration by Substitution is performed by replacing the pronumeral (variable) to other pronumeral to simplify the expression for integrating easier. Students often made mistakes by forgetting to replace back to the original pronumeral.

Practice Questions of Integration by Substitution

Question 1

Find \( \displaystyle \int{\frac{2x}{\sqrt{x^2-4}}}dx \).

Question 2

Find \( \displaystyle \int{\frac{x^2}{\sqrt{1-x^3}}}dx \).

Question 3

Find \( \displaystyle \int{x\sqrt{x^2 + 2}}dx \).

Question 4

Find \( \displaystyle \int{\frac{x}{\sqrt{1-x}}}dx \).

Question 5

Find \( \displaystyle \int{x(x-1)^3}dx \).

Question 6

Find \( \displaystyle \int{x^2(x-4)^4}dx \).