Verified answer

u=1+(2x)^1/2

du=(2x)^-1/2 dx

dx=du(2x)^1/2

du(u-1)

∫1/(du(u)^1/2)

Do all the work and you will get: 1+(2x)^1/2 - ln |1+(2x)^1/2| + c

this is u-substitution, if you really mean √2 * x in the denominator.

Let u = 1 + √2•x

then du = √2 dx

the integral then becomes

1/√2 * ∫1/u du

which you can surely integrate.

ask your teacher in the morning , and next time try to stay awake in class