Question

How to integrate this function?

Answer 1

did you try doing a substitution
\(\Large u = x^2 +1.5^2\)
?

Answer 2

so x / sqrt (u) , and then substitute back the equation after?

Answer 3

sorry, what ?

u = x^2 +1.5^2
du = ... ?

Answer 4

2x

Answer 5

you mean du = 2x dx

Answer 6

and denominator = \(\sqrt u\)
so whats your new integral look like ?

Answer 7

yes.

sqrt (u ) = u ^1/2
2/3 u ^ 3/2

Answer 8

but x dx = du/2, right ?

Answer 9

exactly

Answer 10

yes, i think i get it ty

Answer 11

\[Put \sqrt{x^2+(1.5)^2}=t,x^2=t^2-(1.5)^2,2 x dx=2 t dt,x dx=t dt\]
\[I=\int\limits \frac{ x dx }{ \sqrt{x^2+(1.5)^2} }=\int\limits \frac{ t dt }{ t }=t+c=?\]

Answer 12

i rewrite it.