Basic Rules of integration

Basic Rules of integration

Multiple Choice

Integrate $$\int_{ }^{ }3\ dx$$  

• = 0

• $$=\frac{3}{x}+c$$  

• $$=\ 3x\ +c$$  

• $$=4+c$$  

Multiple Choice

Integrate $$\int_{ }^{ }x^6dx$$  

• $$=6x^5+c$$  

• $$=\frac{x^7}{7}+c$$  

• $$=6x^6+c$$  

• $$=\frac{x^5}{6}+c$$  

Multiple Choice

$$\int6x\left(x+2\right)dx$$  

• $$6x^2+12x+C$$  

• $$x^{2\ }-2x+C$$  

• $$3x^2+6x+C$$  

• $$2x^3+6x^2+C$$

Multiple Choice

$$\int\left(6\sqrt{x}-1\right)dx$$  

• $$6x^{\frac{3}{2}}+x+C$$  

• $$4x^{\frac{3}{2}}-x+C$$  

• $$3x^{-\frac{1}{2}}-x+C$$  

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

Multiple Choice

Find the integral with respect to x of  $$\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$$  

• $$\frac{e^{6x}}{6}\ +\ c$$  

• $$\frac{e^{9x}}{9}\ +\ c$$  

• $$6e^{6x}\ +\ c$$  

• $$\left(e^{3x}\right)^2\ +\ c$$  

Multiple Choice

Find indefinite integral for $$\int_{ }^{ }\frac{1}{e^{5x}}\ dx$$  

• $$\frac{1}{5}e^{5x}\ +\ c$$  

• $$-5e^{4x}\ +\ c$$  

• $$\frac{e^{-5x}}{-5}+\ c$$  

• $$\frac{e^{-4x}}{-4}+\ c$$  

Multiple Choice

Which of the following is TRUE ?

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

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

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

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

Multiple Choice

Integrate $$\int_{ }^{ }\sin x\ dx$$  

• $$=\tan x+c$$  

• $$=-\cos x+c$$  

• $$=-\sec x+c$$  

• $$=\operatorname{cosec}\ x\ +c$$  

Multiple Choice

$$\int_{ }^{ }\frac{\text{1}}{\text{2x}}dx$$  

• $$=\ln2x+c$$  

• $$=2\ \ln2x+c$$  

• $$=\frac{1}{2}\ln2x+c$$  

• $$=\frac{1}{\ln2x}+c$$  

Multiple Choice

$$\int\left(\frac{4}{x}-e_{ }^x\right)dx$$  

• $$\frac{4}{x^2}-xe^x+C$$  

• $$4\ln\left|x\right|-e^x+C$$  

• $$4\ln\left(x\right)-e^x+C$$  

• 
  $$4\ln\left|x\right|+e^x+C$$