Question

Calculus Help!!

Answer 1

Hi, may I help you?

Answer 2

\[\int\limits_{}^{} x \sqrt{x^2+1} dx\]

Answer 3

ah classic integration

Answer 4

So, here we can use the u^n du

Answer 5

Set u to be (x^2+1)
du = 2x dx
dx = du / 2x

Answer 6

so you get\[\int\limits(x \sqrt{u}) * dx/2x\]

Answer 7

now notice the x and the 2x cancel out it becomes now

Answer 8

\[1/2\int\limits(\sqrt{u})du\]

Answer 9

ahh i see now i tried to seperate it into two integrals and just got all turned around deffinetly much clearer! if i got stuck ill b posting some more so keep your eyes peeled

Answer 10

now integrate this normally using integration rules - add 1 to the power, bring the new power to the front.
\[1/2\int\limits(\sqrt{u})du = (1/2)*(3/2)*(u^{3/2}) \]

Answer 11

no problem, thanks! just try to always turn it into u^n du form, makes life much easier

Answer 12

will do!