SOLUTION: I need help with the following promblem, does anyone know about integrals? Find the integral. 4(2x+5)^3 dx

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: I need help with the following promblem, does anyone know about integrals? Find the integral. 4(2x+5)^3 dx      Log On


   

Question 442217: I need help with the following promblem, does anyone know about integrals?
Find the integral.
4(2x+5)^3 dx
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!


Begin with the substitution u = 2x + 5. Since , then this implies that and . We substitute to obtain an integral in terms of u:



This is easily integrable, using the power rule:

where C is a constant. Since we want our expression in terms of x instead of in terms of u, we back substitute to get