Basic Rules of integration

= 0

$$=\frac{3}{x}+c$$  

$$=\ 3x\ +c$$  

$$=4+c$$  

$$=6x^5+c$$  

$$=\frac{x^7}{7}+c$$  

$$=6x^6+c$$  

$$=\frac{x^5}{6}+c$$  

$$6x^2+12x+C$$  

$$x^{2\ }-2x+C$$  

$$3x^2+6x+C$$  

$$2x^3+6x^2+C$$

$$6x^{\frac{3}{2}}+x+C$$  

$$4x^{\frac{3}{2}}-x+C$$  

$$3x^{-\frac{1}{2}}-x+C$$  

I didn't look at my notes to see how to do this one.

$$\frac{e^{6x}}{6}\ +\ c$$  

$$\frac{e^{9x}}{9}\ +\ c$$  

$$6e^{6x}\ +\ c$$  

$$\left(e^{3x}\right)^2\ +\ c$$  

$$\frac{1}{5}e^{5x}\ +\ c$$  

$$-5e^{4x}\ +\ c$$  

$$\frac{e^{-5x}}{-5}+\ c$$  

$$\frac{e^{-4x}}{-4}+\ c$$  

$$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +C$$

$$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ C$$

$$\int_{ }^{ }\ 2x\ \ dx\ =\ x^2\ +C$$

$$\int_{ }^{ }\ \frac{1}{x^2}\ \ dx\ =\ \ln\left|x^2\right|+C$$

$$=\tan x+c$$  

$$=-\cos x+c$$  

$$=-\sec x+c$$  

$$=\operatorname{cosec}\ x\ +c$$  

$$=\ln2x+c$$  

$$=2\ \ln2x+c$$  

$$=\frac{1}{2}\ln2x+c$$  

$$=\frac{1}{\ln2x}+c$$  

$$\frac{4}{x^2}-xe^x+C$$  

$$4\ln\left|x\right|-e^x+C$$  

$$4\ln\left(x\right)-e^x+C$$  

$$4\ln\left|x\right|+e^x+C$$