Thursday

October 23, 2014

October 23, 2014

Posted by **Tracy** on Sunday, June 10, 2007 at 11:10pm.

integral of du/ (u*sqrt(4-u^2))

Thanks again

Use the concept of U substitution!

--Becky Meyers, Harvard Class of 2011

We have to use Trig substition before we can use U substution because it won't work the other way, I tried, I know what the answer is supposed to be I just can't get it.

integral of du/ (u*sqrt(4-u^2))

Substitute u = 1/t. Then

du = -dt/t^2

u*sqrt[4-u^2] = 1/t sqrt[4-1/t^2]

du/ (u*sqrt(4-u^2)) =

-dt/t^2 * t/sqrt[4-1/t^2] =

-dt/[t sqrt(4-1/t^2)] =

-dt/sqrt[4 t^2 - 1]

So, you should do a hyperbolic substitution:

put t = 1/2 cosh(y)

then

dt = 1/2 sinh(y)

sqrt[4 t^2 - 1] = sinh(y)

-dt/sqrt[4 t^2 - 1] = -1/2 dy

The integral is thus y/2 + c =

arccosh(2t) + c =

arccosh(2/u) + c =

Log[2/u + sqrt(4/u^2 - 1)] + c =

Log[2 + sqrt(4 - u^2)] - Log(u) + c =

**Answer this Question**

**Related Questions**

Calculus - Integrate [1/square root of(e^(2x)-1)]. I have to use u substitution...

Calculus - Hi. How can I integrate 1/(X^3 +1) ? Thank you to anyone who can help...

Accounting - I have almost completed my assignment, but am stuck on this ...

Calculus Area between curves - Consider the area between the graphs x+6y=8 and x...

AP Calc AB - how do you use rules for integrals? in general, but I'm just ...

calculus - prove the following integrals: a)sin3xcos7xdx = -1/20cos(10x)+1/8cos(...

calculus showed work - find the area of the rgion bounded by the graphs of y=x^3...

calculus - how do you calculate the instantaneous rate of change. is that the ...

trig - I have heard that trig CAN be super easy, that there are just, like, 10 ...

calculus - [integrals]2/tsqrt(t^4+25) integrals of two over t square root of t ...