Integral of x² √(x³ + 1) dx

[Lo.Lee.Ta.]

∫x^2(√(x^3 + 1))


u = x^3 + 1
du = 3x^2dx
(1/3)du = x^2dx

∫√(u)*(1/3)du

= 2/3(u)^3/2 *(1/3)

= 2/9(x^3 + 1)^3/2

Is this the correct answer? Thank you.

 

[SithsNGiggles]

Yep, looks like it. You can always differentiate your answer if you're not sure.

 

[Mentallic]

∫x^2(√(x^3 + 1))


u = x^3 + 1
du = 3x^2dx
(1/3)du = x^2dx

∫√(u)*(1/3)du

= 2/3(u)^3/2 *(1/3)

= 2/9(x^3 + 1)^3/2

Is this the correct answer? Thank you.

Yes, but don't forget about the constant of integration.

 

[Lo.Lee.Ta.]

Thanks, you guys! :)

That's true. I should differentiate when I'm not sure...

 

[Ray Vickson]

Thanks, you guys! :)

That's true. I should differentiate when I'm not sure...

You should differentiate even when you are sure! (Sometimes a person can be sure but still have the wrong answer.)

In other words: always differentiate!