Find the indicated integral using the method of substitution.
3t[(t^2+8)^1/2] dt

Question

amistre64 · Answer

trig substitution?  or otherwise?

anonymous · Answer

i think he means regular sub

anonymous · Answer

there's no need for a trig id here

amistre64 · Answer

but, but..... i wanna do a trig ;)

anonymous · Answer

rofllls, do the one from this afternoon!

amistre64 · Answer

lol  :)

amistre64 · Answer

3t sqrt(t^2 +8); u = t^2 + 8;  du = 2t dx; dx = du/2t

amistre64 · Answer

3t sqrt(u) du
---------- = (3/2) sqrt(u) du
      2t

anonymous · Answer

3t[(t^2+8)^1/2] dt

u = t^2 + 8
du = 2t dt

$$\frac{3}{2}\int\limits_{}^{}u^{\frac{1}{2}}du = \frac{3}{2}*\frac{2}{3} u ^{\frac{3}{2}} = (t^2 + 8)^{\frac{3}{2}}$$

amistre64 · Answer

(3/2) [S]  u^(1/2) du

(3/2) (2/3) u^(3/2) =  u^(3/2)

anonymous · Answer

i win :P

amistre64 · Answer

yes you do :)   and i added a dx for some reason ;)

anonymous · Answer

it's just variables...i'm used to dx also =/
i hate the fact that they switch up variables...

anonymous · Answer

Thanks!