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**Approach I**is known as the method of integration by direct substitution whereas

**Approach II**is known as the method of integration by indirect substitution.

**Approach I**

Let I=∫f(φ(x))φ'(x)dx

Let z=φ(x)

∴φ'(x)dx=dz

∴I=∫f(z)dz

Approach II

Approach II

Let I=∫f(x)dx

Let x=φ(z)

∴dx=φ'(z)dz

∴I=∫f(φ(z))φ'(z)dz

**My problem:**While i can understand

**Approach I**, I cannot understand

**Approach II**. What is the difference between the two approaches. What is the difference in their usage. I very confused. Please help.