F'(x)=f(x)

F(x)=f(x)

F(x)=f'(x)

$\int_{ }^{ }\lceil f\left(x\right)+g\left(x\right)\rceil=\int_{ }^{ }f\left(x\right)dx+\int_{ }^{ }g\left(x\right)dx$

$\int_{ }k\cdot f\left(x\right)=k\cdot\int_{ }^{ }f\left(x\right)$

$\int_{ }^{ }k\cdot\lceil f\left(x\right)+g\left(x\right)\rceil=k\cdot\int_{ }^{ }f\left(x\right)dx+k\cdot\int_{ }^{ }g\left(x\right)dx$

$\int_{ }^{ }f\left(x\right)\cdot g\left(x\right)\ dx=\ \int_{ }^{ }f\left(x\right)dx\cdot\int_{ }^{ }g\left(x\right)\ dx$

 $3x^3-\frac{6}{x^3}+c$  

 $x^3+\frac{6}{x}+c$  

 $3x^3-\frac{6}{x}+c$  

 $x^3-\frac{6}{x^2}+c$  

 $\frac{x^2}{2}+\frac{2}{3}\ln\left|x\right|-\frac{4}{3}x+c$  

 $x+\frac{1}{x}-\frac{4}{3}+c$  

 $\frac{x^2}{2}+2\ln\left|x\right|-\frac{4}{3}+c$  

 $x+\ln\left|x\right|-\frac{4}{3}+c$  

 $\ln\left(x^2+2x+5\right)+\arctan\ \frac{x}{2}+c$  

 $\frac{1}{2}\ln\left(x^2+1\right)+\arctan\left(\frac{x+1}{2}\right)+c$  

 $\frac{1}{2}\ln\left(x^2+2x+5\right)-\frac{1}{2}\arctan\ \frac{x+1}{2}+c$  

 $\ln\left(x^2+2x+5\right)-\frac{1}{2}\arctan\left(\frac{x+1}{2}\right)+c$