Can anyonw help me find the Integral. ∫ x^3/√(x^2+5) dx?

Question

I just need to know how to start it.

Answer 1

Simple substitution. Let u=x^2 +5. Then du=2xdx and x^2=u-5. The x^3 dx can be written as (u-5)(1/2 du), so you are integrating
Int (1/2) u^(1/2) -(5/2) u^(-1/2) du.
This gives
(1/3) u^(3/2) -5 u^(1/2) +C,
so
(1/3) [x^2 +5]^(3/2) -5 [x^2 +5]^(1/2) +C
is your answer.

Answer 2

well I tried to solve it . but couldn't .

I guess there should be a formula for this in the form

∫ x^b/√(x^2+a) dx

and after applying that formula there would be only 3 or 4 more steps to solve it completely.

ohh I guess above solutions are pretty good

Answer 3

There are only seven types of methods to solve an integral.

if u=x^2+5 then x=sqrt(u-5), du = 2x * dx and dx = du/2x

this gives 0.5*int(x^2/sqrt(u) , du)
or
0.5*int((u-5)*(u^-0.5), du)
or
0.5 *( int(u^3/2,du) + int(5*sqrt(u, du)))

and now its much simpler

Key steps:
-u-substitution
-notice that x^2 is in numerator and x is a function of sqrt(u)
-simpler math
-evaluate integrals
-substitute values
-evaluate numerical expressions

Answer 4

Now that I see your math problem, I totally forgot how to do calculus, but this link may help you.


http://www.webmath.com/nintegrate.html