Integration: int [ x^2 (1 + 9x^2)^(1/2) ] dx

[Syed Zain Uddin]

I need a help if anyone can help me to find out the integration of this or point me in the right directions to do that I'd really appreciate it.

\(\displaystyle \int\, x^2\, \left(1\, +\, 9x^2\right)^{1\,/\,2}\, dx\)

Thank you.

 

[Deleted member 4993]

I need a help if anyone can help me to find out the integration of this or point me in the right directions to do that I'd really appreciate it.
∫x²(1+9x²)^1/2dx

Thank you.

substitute:

\(\displaystyle 3x \ = \ \tan(\theta)\)

or you could use wolframalfa.com

 

[Syed Zain Uddin]

substitute:

\(\displaystyle 3x \ = \ \tan(\theta)\)

or you could use wolframalfa.com

Yeah I substitute this and solve this but answer is not coming like in http://integrals.wolfram.com/

(1/216)[3(1+9x²)^1/2 (18x³ + x) - sinh^-1(3x)]

 

[Deleted member 4993]

Yeah I substitute this and solve this but answer is not coming like in http://integrals.wolfram.com/

(1/216)[3(1+9x²)^1/2 (18x³ + x) - sinh^-1(3x)]

What did you get by integrating?

Please show work.