Sympy integration

Question

I am trying to perform the following integration using sympy;

x = Symbol('x')
expr = (x+3)**5
integrate(expr)

The answer I expect is the following:

But what comes back:

The following code works in MATLAB:

syms x
y = (x+3)^5;
int(y)

I'm not sure what I'm doing wrong to accomplish this using sympy.

Answer 1

This is actually a common problem observed in Calculus, where for these types of polynomial expressions you get two answers. Coefficients for each of the degrees xexist, but there is no constant coefficient between them.

, , , .

• - , u = x+3, u. (1/6)*(x + 3)^6 + C, .

• , .

---

MATLAB :

>> syms x;
>> out = int((x+3)^5)

out =

(x + 3)^6/6

-, , , , , :

>> expand(out)

ans =

x^6/6 + 3*x^5 + (45*x^4)/2 + 90*x^3 + (405*x^2)/2 + 243*x + 243/2

---

sympy :

In [20]: from sympy import *

In [21]: x = sym.Symbol('x')

In [22]: expr = (x+3)**5

In [23]: integrate(expr)
Out[23]: x**6/6 + 3*x**5 + 45*x**4/2 + 90*x**3 + 405*x**2/2 + 243*x

---

, , . , , , MATLAB.

, , sympy, , . , sympy :

>> syms x;
>> out = expand((x+3)^5)

out =

x^5 + 15*x^4 + 90*x^3 + 270*x^2 + 405*x + 243

>> int(out)

ans =

x^6/6 + 3*x^5 + (45*x^4)/2 + 90*x^3 + (405*x^2)/2 + 243*x

, . , , , .

---

DSM, manual=True integrate, , , :

In [26]: from sympy import *

In [27]: x = sym.Symbol('x')

In [28]: expr = (x+3)**5

In [29]: integrate(expr, manual=True)
Out[29]: (x + 3)**6/6