Question

How do you find the integral of `x*sqrt(25+x^2)`?

Answer 1

Have a look but please check my maths:

Answer 2

`int xsqrt(25 + x^2)dx = int1/2*2xsqrt(25 + x^2)dx`

`= int1/2sqrt(25 + x^2)*(2xdx)`
`= int1/2sqrt(25 + x^2)*d(25 + x^2)`

`=1/2int(25 + x^2)^(1/2)*d(25 + x^2)`

`= 1/2((25 + x^2)^(3/2))/(3/2) + c`

`=((25 + x^2)^(3/2))/3 + c`