- #1

chwala

Gold Member

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- Homework Statement:
- I am looking at the integration of ##(x+2)^2## with respect to ##x##

- Relevant Equations:
- Integration

Ok i know that,

##\int (x+2)^2 dx= \int [x^2+4x+4] dx= \dfrac{x^3}{3}+2x^2+4x+c##

when i use substitution;

i.e letting ##u=x+2## i end up with;

##\int u^2 du= \dfrac{u^3}{3}+c=\dfrac {(x+2)^3}{3}+c=\dfrac{x^3+6x^2+12x+8}{3} +c##

clearly the two solutions are not the same...

appreciate your insight...which approach is more concrete? note that when we differentiate both solutions we get the same function i.e ##x^2+4x+4##.

##\int (x+2)^2 dx= \int [x^2+4x+4] dx= \dfrac{x^3}{3}+2x^2+4x+c##

when i use substitution;

i.e letting ##u=x+2## i end up with;

##\int u^2 du= \dfrac{u^3}{3}+c=\dfrac {(x+2)^3}{3}+c=\dfrac{x^3+6x^2+12x+8}{3} +c##

clearly the two solutions are not the same...

appreciate your insight...which approach is more concrete? note that when we differentiate both solutions we get the same function i.e ##x^2+4x+4##.