Question

Using u substitution, integrate S x(sqrt(x^2 + 1))dx

Answer 1

I'm guessing that your S is actually the integral sign (∫)

Answer 2

yes, sorry

Answer 3

can you help me walk through this?

Answer 4

Use the substitution x = tan(u).

Answer 5

So x^2 + 1 = tan^2u + 1 = sec^2u & dx = sec^2u. Now, sub. these values into the integral & evaluate it. Can you try this?

Answer 6

wait a minute, trig? it's a square root

Answer 7

We can use substitution to change a function in an integral - this is one of the intricacies of calculus ...

Answer 8

u = x^2 + 1
du = 2x dx
1/2 du = x dx
this seems much easier

Answer 9

@cleetus779 : Oh yes, you can do this as well ... :p

Answer 10

came up with sqrt(u^3)/3 is that right?

Answer 11

It should be sqrt(u^3)/4 + c (where c is an arb. const).

Answer 12

But that's not the final answer - you should re-substitute the u back as a function of x, since the original question was using x, not u. Can you express your final answer in terms of x?

Answer 13

ok, thanks for the help

Answer 14

double checked here http://www.wolframalpha.com/input/?i=integrate+x%28sqrt%28x%5E2+%2B+1%29%29