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 x 2 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( x 2 )dx Now you can notice that 2x is the derivative of inner function of cos i.e. x 2 . 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. Re...