SOLUTION: I need help with the following promblem, does anyone know about integrals?
Find the integral.
4(2x+5)^3 dx
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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) (Show Source): You can put this solution on YOUR website!
^3\,dx)
Begin with the substitution u = 2x + 5. Since 
, then this implies that 
and 
. We substitute to obtain an integral in terms of u:
 = \frac{1}{2} \int 4u^3\, du)
This is easily integrable, using the power rule:
 + C = \frac{u^4}{2} + C)
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
^3\, dx = \frac{(2x+5)^4}{2} + C)
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