- #1

fantomas2005

- 4

- 0

x^2 cos (x^5) dx

i tried integration by parts but i didn't get anything

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- Thread starter fantomas2005
- Start date

- #1

fantomas2005

- 4

- 0

x^2 cos (x^5) dx

i tried integration by parts but i didn't get anything

- #2

rootX

- 465

- 4

some mess:

f =

x^2*cos(x^5)

>> int(f,x)

ans =

1/10*2^(3/5)*pi^(1/2)*(5/3/pi^(1/2)/x^2*2^(2/5)

*sin(x^5)+5/3/pi^(1/2)/x^2*2^(2/5)*(cos(x^5)

*x^5-sin(x^5))-2/3/pi^(1/2)*x^8*2^(2/5)/(x^5)^(11/10)

*sin(x^5)*LommelS1(1/10,3/2,x^5)-5/3/pi^(1/2)*x^8

*2^(2/5)/(x^5)^(21/10)*(cos(x^5)*x^5-sin(x^5))

*LommelS1(11/10,1/2,x^5))

>> f = x^2*(cos(x))^5

f =

x^2*cos(x)^5

>> int(f,x)

ans =

x^2*(1/5*cos(x)^4*sin(x)+4/15*cos(x)^2*

sin(x)+8/15*sin(x))+2/25*x*cos(x)^5-2/125*

cos(x)^4*sin(x)-272/3375*cos(x)^2*sin(x)-4144/3375*

sin(x)+8/45*x*cos(x)^3+16/15*x*cos(x)

- #3

fantomas2005

- 4

- 0

and the original problem is from my exam {{ and i didn't solve it but I'm curious }}

given____ { int from 0 to 4 }{int from y^1/2 to 2 } cos(x^5) dx dy ____ reverse the order of integration and evaluate the resulting intgerals .

after reversing , it will be ______ x^2 cos (x^5) dx _______ and the inequalities dosent matter

- #4

Vid

- 402

- 0

You reversed the order of integration. You intergrate with wrt y first, dydx.

Last edited:

- #5

fantomas2005

- 4

- 0

so what is the solution of the integration pls

- #6

Kurdt

Staff Emeritus

Science Advisor

Gold Member

- 4,846

- 6

- #7

fantomas2005

- 4

- 0

i'm absolutely sure that it's int of x^2 cos(x^5) dx

dose anyone have any idea ??

dose anyone have any idea ??

- #8

dirk_mec1

- 761

- 13

What was the original question? We've already proved that the integral you post is too difficult!

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