Answer:
Step-by-step explanation:
The antiderivative for b is definitely incorrect, as stated in the comments section.
[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex] That's a bit more simplified. One more important simplification and then we can integrate one term at a time:
[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex] and here we go:
[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and
[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,
[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]
