Question

Integrate:

Answer 1

\[\large \int\limits_{}^{}e^{x^{4}}(x+x^3+2x^5)e^{x^{2}}dx\]

Answer 2

is this an indefinite integral ?

Answer 3

yes

Answer 4

then the error function isnt going to work

Answer 5

can you simplfy the integrand?

Answer 6

i don't know

Answer 7

try by parts separately or use this | e^x (f(x)+f`(x)) = e^x(f(x))

Answer 8

what's f(x) here?

Answer 9

this is what you have to find.... :D

Answer 10

that you got to find
int e^(g(x)) (g'(x)f(x)+f'(x)) = e^(g(x))f(x)

Answer 11

put g(x) = x^4 + x^2
and g'(x) f(x) + f'(x) = 2x^5+x^3+x, put the value of g'(x) and find f(x)

Answer 12

i'm not getting pls you solve

Answer 13

http://www.wolframalpha.com/input/?i=%284x%5E3%2B2x%29+f%28x%29+%2B+f%27%28x%29+%3D+2x%5E5%2Bx%5E3%2Bx

Answer 14

look for the particular solution of f(x) that is x^2/2
that should give you your answer is e^(g(x)) x^2/2

Answer 15

we have not studied diff. eq. ,so isn't there any other way to solve?

Answer 16

this is just integration by parts. if you manipulate things carefully you should get the solution. best is to guess your solution that your solution will be of the form e^(x^4+x^2) (ax^2+bx+c)

Answer 17

differentiate it and compare values and solve for a,b,c ... you can guess that your solution will be of the form because the polynomial term is or order ^5

Answer 18

if it were less than x^3, i.e. e^(x^4+x^2) (x^2 + x + c) then an educated guess would be that it wouldn't be integrable in elementary terms.