Solve for C: Find Value of Line Segment in 3D Graph

[Weatherkid11]

Find the exact value of http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129112586326885897811250007777.gif where http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129110356326885883583125005816.gif and C is the line segment from (1,2,1) to (6,4,5).
i, j, k are unit vectors
So far all i have done is drawn in the line segment on a 3D graph.. Look at the URLS for the integral and the F(x,y,z)

 

[amcavoy]

Find the exact value of http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129112586326885897811250007777.gif where http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129110356326885883583125005816.gif and C is the line segment from (1,2,1) to (6,4,5).
i, j, k are unit vectors
So far all i have done is drawn in the line segment on a 3D graph.. Look at the URLS for the integral and the F(x,y,z)

\int_C\mathbf{F}\cdot d\mathbf{r}

\mathbf{F}=\left<x^4e^y,\,\ln{z},\,\sqrt{y^2+z^2}\right>

\mathbf{r}=\left<1+5t,\,2+2t,\,1+4t\right>;\quad 0\leq t \leq 1

Can you figure it out from here?

 

[Weatherkid11]

OK i worked off of what you got and i got
http://www.freemathhelp.com/forum/mimetex/pictures/d1183703930c2d1a7c5a37255ca42e49.gif
But this integral looks VERY hard to solve

 

[arildno]

OK i worked off of what you got and i got
http://www.freemathhelp.com/forum/mimetex/pictures/d1183703930c2d1a7c5a37255ca42e49.gif
But this integral looks VERY hard to solve

A few hints:
For the first term, use integration-by-parts, and for the third term, complete the square in the form: K\sqrt{(t+a)^{2}+b}, where K,a,b are appropriate constants. Dependent upon the sign of b, we may write b=\pm{c}^{2} where c is some constant.

See if you manage to make the last few steps on your own..