Question

What is the antiderivative of `f(u) = (u^4 + 3sqrtu) / u^2`?

Answer 1

`1/3u^3-6/sqrtu+c`

Explanation:

`>"simplify f(u) by splitting the numerator"`

`f(u)=u^4/u^2+(3u^(1/2))/u^2`

`color(white)(f(u))=u^2+3u^(-3/2)`

`"integrate using the "color(blue)"power rule"`

`• int(ax^n)=a/(n+1)x^(n+1);n!=-1`

`rArrint(u^2+3u^(-3/2))dx`

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

`=1/3u^3-6/sqrtx+c`

`"where c is the constant of integration"`