Sympy how to define variable for functions, integrals and polynomials

## Check if variable is well defined

$\displaystyle e^{x} \sin{\left(x \right)}$

## v is not defined

Since v is not defined, we got an error:

## Define polynomial use ** and not symbol ^

$\displaystyle x^{4} - 3 x^{2} + 15 x - 1$

Oups … You got an error …

Remember that ^ is a logic binary operator:

0b1 0b1010 True 11 0b1011

## First way to define an function

Check f(3) value:

10

## Second way to define a function

Check g(3) value:

10

## Calculate an integral

$\displaystyle \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$

$\displaystyle \frac{t^{2} e^{t} \sin{\left(t \right)}}{2} + \frac{t^{2} e^{t} \cos{\left(t \right)}}{2} - t e^{t} \sin{\left(t \right)} + \frac{e^{t} \sin{\left(t \right)}}{2} - \frac{e^{t} \cos{\left(t \right)}}{2}$

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

Remember how g was defined !!!!

Here is the good way to integrate it:

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

That’s all folks !!! Below , jupyter’s notebook.