To Take An Antiderivative By Substitution 

 Declare the "inside function" to be u.
 Take the derivative of u.
 Divide by dx, the differential of x to isolate du, the differential of u.
 Isolate the dx and any factors containing x on one side of the equation so it is (possible x factors)(dx).
 If needed, multiply or divide both sides by a constant so (possible x factors)(dx) is alone  isolated  on one side.
 Go back to the original integral.
 Put u in place of the original function.
 Remove the (possible x factors)(dx) expression, and replace it with the its equivalent expression which includes du.
 If the problem is a definite integral, rewrite the bounds of integration in terms of u, not x.
the new upper bound b = u(b)
the new lower bound a = u(a)
 Integrate the rewritten integral.
 If the problem is an indefinite integral, rewrite the result in terms of x, and add the + C.
