Integration by Substitution (1 Viewer)

[Smilebuffalo]

integrate sqrt(x)/(x*sqrt(x) +2) u = x*sqrt(x)

 

[life92]

lol soz
iuno how to use latex but,,

u = x root x = x^3/2

therefore, du = (3/2) x^(1/2) dx

then

integral x^(1/2) / [ x^(3/2) + 2 ] dx

= 2/3 integral 1 / (u+2)
= 2/3 ln (u+2)
= 2/3 ln [ x^(3/2) + 2 ] + c

 

[Smilebuffalo]

ty