Basic Integral Theorems

C

ax

ax+C

axdx

$$a\int_{ }x\ dx$$

$$ax^2+C$$

ax + C

$$\frac{ax^2}{2}$$

$$\frac{x^n}{n}+C$$

$$\frac{x^{\left(n-1\right)}}{\left(n-1\right)}+C$$

$$\frac{x^{\left(n+1\right)}}{\left(n+1\right)}+C$$

$$x^{\left(n+1\right)}+C$$

$$a^x\ln a+C$$

$$a^x\ln x+C$$

$$\frac{a^x}{\ln x}+C$$

$$\frac{a^x}{\ln a}+C$$

not defined

indeterminate

$$e^x+C$$

$$\ln x+C$$

$$7^x\ln7+C$$

$$7^x\ln x+C$$

$$\frac{7^x}{\ln7}+C$$

$$\frac{7^x}{\ln x}+C$$

$$\ln\ 5x\ +\ C$$

$$5\ \ln\ x\ +\ C$$

$$\frac{\ln\ x}{5}+C$$

$$\ln\ \frac{5}{x}+C$$

$$\frac{x^6}{6}$$

$$\frac{x^6}{3}$$

$$\frac{x^6}{6}+C$$

$$\frac{x^6}{3}+C$$

$$\frac{4}{7}x^{\frac{7}{4}}+C$$

$$\frac{7}{4}x^{\frac{7}{4}}+C$$

$$\frac{3}{7}x^{\frac{7}{3}}+C$$

$$\frac{3}{7}x^{\frac{3}{7}}+C$$

$$\frac{3}{5}x^5+C$$

$$\frac{1}{x^3}+C$$

$$\frac{-1}{x^3}+C$$

$$\frac{3}{x^3}+C$$