decimal to fraction calculator

Example 5${\displaystyle \int7x^{4/3}dx=7\int x^{4/3}dx=7\frac{x^{4/3+1}}{\frac{4}{3}+1}=3x^{7/3}+\mathrm{c}}$, where $c$ is an arbitrary constant of integration. Example 6${\displaystyle \int\{3x^{2}+1+\frac{1}{x^{2}}\}dx=\int3x^{2}dx+\int1dx+\int\frac{1}{x^{2}}dx}$   $=3\cdot\frac{x^{3}}{3}+c_{1}+x+c_{2}+\frac{x^{-2+1}}{-2+1}+c_{3}=x^{3}\prime+x-\frac{1}{x}+c,$ where $c(=c_{1}+c_{2}+c_{3})$ is an arbitrary constant of integration. Note. There is no need to introduce an arbitrary constant after calculating each integral (as is done in the above example). By combining all arbitrary constants, we get a single arbitrary constant denoted by $c$ which is added to the final answer. Example 7${\displaystyle \int(2\cos2x+\frac{3}{x}-9e^{x})dx=2\int\cos2xdx+3\int\frac{1}{x}dx-9\int e^{x}dx}$ $=2{\displaystyle \frac{\sin2x}{2}+3\log|x|-9e^{x}+c=\sin2x+3\log|x|-9e^{x}+c}$, where $c$ is an arbitrary constant of integration. Example 8${\displaystyle \int\frac{(2x-3)^{3}}{x^{2}}dx=\int\frac{8x^{3}-36x^{2}+54x-27}{x^{2}}dx}$ $=8{\displaystyle \int xdx,-36\int dx+54\int\frac{1}{x}dx-27\int\frac{1}{x^{2}}dx}$  $=4x^{2}-36x+54{\displaystyle \log|x|+\frac{27}{x}+c}$, where $\mathrm{c}$ is an arbitrary constant of integration. Example 9$\int \left (3\sec 3x\tan 3x-8e^{8x}+20\sec ^2 20x+\frac {5}{\sqrt {1-x^2}} \right )dx$  $=3\cdot\frac{\sec3x}{3}-8\cdot\frac{e^{8x}}{8}+20\cdot\frac{\tan20x}{20}+5\sin^{-1}x+c$  $=\sec3x-e^{8x}+\tan20x+5\sin^{-1}x+c,$ where $c$ is an arbitrary constant of integration. Example 10 Find $y$ when $dy/dx=x^{\dot{2}}$. $dy=x^{2}dx$ and hence${\displaystyle \int dy=\int x^{2}dx}$, or,   $y={\displaystyle \frac]{3}x^{3}+c}$.