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

1 Answer
May 18, 2017

#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"#