Question

Evaluate the indefinite integral :

Answer 1

\[\int\limits (x^3 + \frac{ 4 }{ x^2 } - e^{-2x}) dx\]

Answer 2

Hi Chloro! :)

Answer 3

Can I show you what I did?

Answer 4

\[\frac{ x^4 }{ 4 }\]

Answer 5

\[- \frac{ 4 }{ x }\]

Answer 6

Can i ask, how does 4/x^2 become -4/x again?

Answer 7

No,I followed a rule :D

Answer 8

1/a^b = a^-b

Answer 9

so 4x ^ -2?

Answer 10

Ok, back to the equation :D

Answer 11

-e^-2x

= 1/2e ^-2x?

Answer 12

\[e^{ax} = \frac{ 1 }{ a } e^{ax}\]

Answer 13

?

Answer 14

\[\frac{1}{2e^{2x}} + \frac{x^4}{4} - \frac{4}{x} + C\]

Answer 15

you have all the right ideas, just put them together!

Answer 16

How do i get 1/2e^-2x to 1/2e^2x mate?

Answer 17

you know that \[e^{-2x} = \frac{1}{e^{2x}} \] right? so just integrate that as you would normally

Answer 18

I think about it interms of the antiderivative, ie. what would i take the derivative of to get this.

Answer 19

1/2 goes under the line and becomes 2 then?

Answer 20

well you get 1/2 * 1/e^2x so kinda!

Answer 21

Could I ask you a quick question?

Answer 22

sure