Question

Hw to integrate x^2.e^x^(3-1)

Answer 1

Do i use product rule

Answer 2

is the question
\(\huge \int x^2 e^{x^3-1}dx\)
?

Answer 3

Yes

Answer 4

then do a simple 'u' substitution,no need of integration by parts

Answer 5

\(\Large u = x^3-1\)
du =... ?

Answer 6

3x

Answer 7

just 3x ?

u = x^3-1
differentiate w.r.t x,

du/dx =... ?

Answer 8

3x^2

Answer 9

correct

so,

du/dx = 3x^2
but in the question we have

x^2 dx

Answer 10

Yea

Answer 11

so,

du = 3x^2 dx

x^2 dx = du/3

got this ?

Answer 12

Oh yes

Answer 13

now whats your new integral, only in 'u' ?

Answer 14

Why differentiating when asked to integerate

Answer 15

we are changing the variable from 'x' to 'u'

so we need to find du in terms of dx

to find du, we need to differentiate u

Answer 16

while doing substitution, we need to completely change the function, including dx

Answer 17

X^2. e^(3x^2-1)

Answer 18

?

there should be no 'x' in your new function