Integration by U-substitution

When finding antiderivatives, we are basically performing "reverse differentiation." Some cases are pretty straightforward. For example, we know the derivative of x2 is 2x.

On the other hand, There is not a simple case every time. For example,∫ cos(3x+5)dx ? It will never equal to the sin(3x+5) + c. So we have tp adopt other method to integrate it. One method that can be very useful is u-substitution method.

The U-substitution method id basically the inverse of the chain rule method.

How to Solve by U-substitution?

Consider we have to find the integral of following:

∫ 2x cos(x2)dx

Now you can notice that 2x is the derivative of inner function of cos i.e. x2. In general, we will substitute the inner function with the simpler function i.e. "u".

This is generally known as u-substitution method. We can try online u-substitution calculator to solve such type of integral
problems online without any difficulty.

Related: Also read integration by u substitution & it's related technology.