Question

please help me integrate this :

Answer 1

\[56x^{13} e^{-x^{14}}\]

Answer 2

did you try a subsitution

Answer 3

let u=-x^(14)

Answer 4

yeah it says i should use substitution rule but im still confused.

Answer 5

well if u=-x^(14) then du/dx=?

Answer 6

i already have the answer, but i want to know how to get there

Answer 7

\[u=-x^{14} \\ \frac{du}{dx}=?\]

Answer 8

you know power rule

Answer 9

use it to find the derivative of -x^(14)

Answer 10

is it -x^15 / 15 ?

Answer 11

derivative of -x^(14)?

Answer 12

oh wait sorry thats wrong

Answer 13

yeah sorry i saw it wait im gonna give you another answer

Answer 14

-14x^13 hows that?

Answer 15

\[(c \cdot x^{n})'=c (x^{n})'=c \cdot n x^{n-1}\]
this is power rule for differentiating
yes that!

Answer 16

\[u=-x^{14} \\ \frac{du}{dx}=-14 x^{13} \\ du=-14x^{13} dx \\ -4 du=56 x^{13} dx\]

Answer 17

can you finish now?

Answer 18

yes thank you!