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# integration by subsitution watch

1. u =ln x , find the integral of 1/x(lnx)^1/2 with e^4 at the top and e at bottom

is this right?

du/dx = 1/e^u

x =e^u

u=4, x=e^4
u=1, x =e

the integral is 1/e^u(u)^1/2 x e^u du

so integral with 4 at top and 1 at bottom = 1/(u)^1/2

so [2u^1/2] with 4 at top and 1 t bottom

= 2
2. (Original post by Custardcream000)
u =ln x , find the integral of 1/x(lnx)^1/2 with e^4 at the top and e at bottom

is this right?

du/dx = 1/e^u

x =e^u

u=4, x=e^4
u=1, x =e

the integral is 1/e^u(u)^1/2 x e^u du

so integral with 4 at top and 1 at bottom = 1/(u)^1/2

so [2u^1/2] with 4 at top and 1 t bottom

= 2
Yes. That's correct.

And you might want to try using LaTex (link in "Useful resources" widget to the side) - it would make your post more readable.
3. (Original post by Custardcream000)
u =ln x , find the integral of 1/x(lnx)^1/2 with e^4 at the top and e at bottom

is this right?

du/dx = 1/e^u

x =e^u

u=4, x=e^4
u=1, x =e

the integral is 1/e^u(u)^1/2 x e^u du

so integral with 4 at top and 1 at bottom = 1/(u)^1/2

so [2u^1/2] with 4 at top and 1 t bottom

= 2
http://www.thestudentroom.co.uk/wiki/LaTeX

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