Head scratching integral calculus hw

[JasonJo]

hey guys, i need help on my integral calculus hw

2) int(x*3*e^(x^7)) dx
this one is just giving me insane problems

 

[cepheid]

1) Try the substitution:

u = (4-t)^1/2

du = -dt / 2(4-t)^1/2

Key thing here: you've got some expression of t and square root of some other expression involving t. Make a substitution to so that u is proportional to square root of t, and therefore t is in terms of u^2, and your integral now has u and u^2 in it. Much easier to work with. No square roots. Just polynomials. That's why I chose that substitution.

 

[scholzie]

2) int(x*3*e^(x^7)) dx
this one is just giving me insane problems

Is this $$\int3 x e^x^7{dx}$$ or $$\int x^3 e^x^7{dx}$$?

As you have it written, it's a very strange order for multiplication. Either way, it doesn't seem to be a simple, straight-forward answer. The only way I seem to have found so far requires a reduction formula.

 

[dextercioby]

For the integral
$$\int x \ e^{x^{7}} dx$$

view the first attachement.

For the integral
$$\int x^{3} \ e^{x^{7}} dx$$

view the second...

Daniel.

 

[scholzie]

For the integral
$$\int x \ e^{x^{7}} dx$$

view the first attachement.

For the integral
$$\int x^{3} \ e^{x^{7}} dx$$

view the second...

Daniel.

If he's still doing normal substitutions, it is doubtful that he is expected to know gamma integral transformations. I think there's a typo in the original poster's post.

 

[dextercioby]

Then let him correct it,else his entire visit to PF has been useless...

Daniel.