Question

Hi, does anyone know how to find the most general antiderivative or indefinite integral of a fraction with variables on the top and bottom. Ex: t times t^1/2 + t^1/2 all over t^2

Answer 1

\[\huge \int\limits_{}^{}\frac{t(t^{\frac{1}{2}})+t^{\frac{1}{2}}}{t^2}dt~~~???\]

Answer 2

yep

Answer 3

wow that is a big one

Answer 4

\[\huge \int\limits_{}^{}\frac{t(t^{\frac{1}{2}})+t^{\frac{1}{2}}}{t^2}dt\]
\[\huge \int\limits_{}^{}\frac{(t^{\frac{3}{2}})+t^{\frac{1}{2}}}{t^2}dt\]
\[\huge \int\limits_{}^{}\frac{(t^{\frac{3}{2}})}{t^2}+\frac{t^{\frac{1}{2}}}{t^{2}} dt\]
\[\huge \int\limits\limits_{}^{}t^{-1/2}+t^{-3/2}~~dt\]

Answer 5

Then just integrate each term

Answer 6

Oh wow, thanks - I tried finding the antider. before dividing...not my brightest moment. Thanks :)