Question

Indefinite Integrals.....

indefinite integral (x+1)(3x-2) (dx)

1st thing I did was "distribute" using FOIL.
and then I got stuck because of what I have left

3x^2 + x -2 (dx)

What next?

Answer 1

you can break up the integral like this
\[\Large \int (3x^2 + x - 2)dx = \int (3x^2)dx+\int (x)dx + \int (-2)dx\]

Answer 2

@jim_thompson5910 ok that looks good, but what about the 3x^2 part?

Answer 3

you can pull out the coefficient

\[\Large \int (3x^2)dx = 3*\int (x^2)dx\]

Answer 4

for x(dx) = x^2/2 and for (-2) =-2x

Answer 5

A lot of rules that you find with differentiating are similar in integration

Answer 6

correct on both of those

Answer 7

so everytime I see a number infront of the variable I pull it outside the integral sign as you did above?

Answer 8

correct

Answer 9

\[\Large \int k*f(x)dx = k*\int f(x) dx\]

where k is a constant

Answer 10

this is what I got as my final answer:

\[\frac{ 3x^{3} }{ 3 } + \frac{x ^{2} }{ 2 } -2x\]

Answer 11

the 3x^3 over 3 reduces to x^3

Answer 12

and don't forget the +C

Answer 13

oh yes okay, does first one simplify to x^3 ?

Answer 14

yes it does

Answer 15

Ok great! Thank you so much!! @jim_thompson5910

Answer 16

you're welcome