Antidifferentiation?

Question

Given that f(x) = (2x + 5)^3 find

∫ f(x)dx

step by step explanation please

Answer 1

∫ f(x)^ndx  = f(x)^n+1/n*df(x)/dx

∫ (2x + 5)^3 = (2x + 5)^4/4*2 + C

(2x + 5)^4/8 + C

Answer 2

Let (2x+3) = u

2 dx = du

dx = (1/2) du

∫ f(x)dx =(1/2) ∫ u^3 du

=u^4/4 +C

=(2x+5)^4 / 4 (1/2)

=(2x+5)^4 / 8 +C

Answer 3

f(x) = (2x + 5)^3.

∫  f(x).dx = ∫ (2x+5)^3 . dx

put u = 2x + 5

     du = 2.dx

∫ f(x).dx =  ÃƒÂ¢Ã‚ˆÂ« u^3. du/2

            = 1/2* (u^4)/4 + C

           = (2x + 5)^4 / 8 + C.

Answer 4

Another word for integration.

Ask your teacher.