Integral Calculation - Get Help Solving Problems

[cataldo]

I have some problem with following integral. In attachment a pdf with integral..
I have done a integration by sobstitution but i have not a result ...
Tank for your in interest
best regards

 

[tiny-tim]

why couldn't you type that out?

try substituting so that sin becomes cos of something else.

 

[cataldo]

Ok...
I have done this question because the calculate on site "wolfram mathematica online integrator" only indefinite integral is very complicated and i don't understand as i can obtain this...
Cataldo...

 

[mathman]

By a little manipulation you can transform it into an integral from 0 to 1 of the following:

2[(1+x)^1/2 + [(1-x)^1/2]/(1-x²). Essentially this was done by collapsing the integral into 0 to pi/2 and then letting x=sin.

See if you can go further.

 

[cataldo]

Ok...Tanks mathman
Is exactly x=sin and integral from 0 to 1.. but i obtain [(1+x)^(1/2)]/(1-x^2)... Does it correct?

 

[tiny-tim]

why couldn't you type that out?

try substituting so that sin becomes cos of something else.

how about sinx = cos(π/2 - x)?

 

[mathman]

Ok...Tanks mathman
Is exactly x=sin and integral from 0 to 1.. but i obtain [(1+x)^(1/2)]/(1-x^2)... Does it correct?

The sin is positive from 0 to pi and negative from pi to 2pi. I first collapsed the second interval into the first, so I had two terms: 1+sin and 1-sin. Next collapsing to 0 to pi/2 with a factor of 2. Finally let x=sin.

 

[cataldo]

Hi nathaman..Tanks for your replay
I understand your method but the software mathematica can not assess the definte integral because the fuction between 0 to 1 not converge...exist the indefinte integral indeed mathematica assess it... I think that is necessary assess it by numerical integration...