Need help with an integral (substitution)

[fernlund]

Hello! I need help to integrate the square root of (p*x^2 + x^4) by the method of substitution. So, (p*x^2 + x^4)^1/2 where p is just a constant. Any tips? I know the answer is (p*x^2 + x^4)^(3/2) / (3 x^3) but it doesn't really help me.

 

[Deleted member 4993]

Hello! I need help to integrate the square root of (p*x^2 + x^4) by the method of substitution. So, (p*x^2 + x^4)^1/2 where p is just a constant. Any tips? I know the answer is (p*x^2 + x^4)^(3/2) / (3 x^3) but it doesn't really help me.

\(\displaystyle \sqrt{p*x^2 + x^4} \ = x * \sqrt{p + x^2}\)

Now substitute

u = p + x²

a little algebra and you'll be there...

 

[HallsofIvy]

Strictly speaking, that should be \(\displaystyle \sqrt{px^2+ x^4}= |x|\sqrt{p+ x^2}\).