Integration: integral (arcsin(1/x)dx), integral (x^3*sqrt...

[Clifford]

I have having trouble with these integrals. Looking for somebody to start them for me or let me know the substutions to use. I have tried substitutions as well as by parts several times on them and am getting no where.

integral (arcsin(1/x)dx)

integral (x^3*sqrt(4-x^2)dx)

integral (x^2 / [(x^2 + a^2)^3/2] dx)

Thanks

 

[Deleted member 4993]

Re: Integration

I have having trouble with these integrals. Looking for somebody to start them for me or let me know the substutions to use. I have tried substitutions as well as by parts several times on them and am getting no where.

integral (arcsin(1/x)dx) ..............................substutute u = arcsin(1/x)

integral (x^3*sqrt(4-x^2)dx) ........................substitute x = 2* sin(u)

integral (x^2 / [(x^2 + a^2)^3/2] dx) .............substitute x = a * tan(u)

Thanks

 

[Clifford]

Re: Integration

These ones are harder than I thought.
I can't get the last or first one.

For the 2nd one I have 32* integral (sin^3u * cos^2u)
but I am not sure where to go from here. I don't even know if its right up to that point.

 

[Deleted member 4993]

Re: Integration

These ones are harder than I thought.
I can't get the last or first one. .....Show your attempts..

For the 2nd one I have 2* integral (sqrt(sinu * 2cos^2u du)) ....How are you getting sqrt? show detail...


but I am not sure where to go from here. I don't even know if its right up to that point.

 

[Clifford]

Re: Integration

Could you tell me which kind of substitution to use for each one?

Plain, by parts of trig?

 

[Deleted member 4993]

Re: Integration

Could you tell me which kind of substitution to use for each one?

Plain, by parts of trig?

To me, substitutions are always plain - and I have given you the variables and functions to be substituted.