Integrating square roots

[scott73]

I need some help with a few of these problems, first I cannot seem to get started on the problem of integrating (sin(sqrt(x)))dx, I just cannot find a way to do it!
Second, I am having trouble even finding what method to use in the integral of 1/(x^2 + 2), you cant use a trig substitution cause it isnt under a square root sign.
Third, I cannot seem to find the right substitution for the integral,
x^3/(sqrt(49-x^2)), I know that you may be able to use some form of trig substitution but I dont know how to do it with the x^3 on the top, thank you for any help!

 

[stapel]

1) int [sin(sqrt(x))] dx

Try a u-substitution, with sqrt(x) = u, so x = u² and dx = 2u du. Then integrate the result by parts.

2) int [1/(x² + 2)] dx

You can do a trig substitution: review your inverse-trig-function derivatives for a hint on how to proceed.

3) int [x³/sqrt(49 - x²)] dx

Hint: Let x = 7sin(ß).

Eliz.

 

[scott73]

Hey I am still having a difficult time with these problems,
for the first one int. of sin(sqrt(x)) I did use the sqrt(x) as my u and then set 2u du equal to dx. this gives 2u(sin(u)) as my integral. then I did integration by parts and came up with -2ucos(u) - 2sinu, where did I go wrong, I got the wrong answer.

for the second problem 1/(x^2 + 2) I realized that this looks like inverse of tangent, but I cannot get it into the form 1/(x^2 +1) which is required, so if you have any additional hints on that one it would be appriciated.