Answer
a. $F(x)=\frac{1}{\sqrt 3+1}x^{\sqrt 3+1}+C$
b. $F(x)=\frac{1}{\pi+1}x^{\pi+1}+C$
c. $F(x)=\frac{1}{\sqrt 2}x^{\sqrt 2}+C$
Work Step by Step
a. Given $f(x)=x^{\sqrt 3}$, we have $F(x)=\frac{1}{\sqrt 3+1}x^{\sqrt 3+1}+C$ as its antiderivative, where $C$ is a constant.
b. Given $f(x)=x^{\pi}$, we have $F(x)=\frac{1}{\pi+1}x^{\pi+1}+C$ as its antiderivative, where $C$ is a constant.
c. Given $f(x)=x^{\sqrt 2-1}$, we have $F(x)=\frac{1}{\sqrt 2}x^{\sqrt 2}+C$ as its antiderivative, where $C$ is a constant.
