Question

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

Answer 1

trig substitution? or otherwise?

Answer 2

i think he means regular sub

Answer 3

there's no need for a trig id here

Answer 4

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

Answer 5

rofllls, do the one from this afternoon!

Answer 6

lol :)

Answer 7

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

Answer 8

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

Answer 9

3t[(t^2+8)^1/2] dt

u = t^2 + 8
du = 2t dt

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

Answer 10

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

(3/2) (2/3) u^(3/2) = u^(3/2)

Answer 11

i win :P

Answer 12

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

Answer 13

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

Answer 14

Thanks!