Status: New
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Labels: Type-Defect Priority-Medium

New issue 2477 by [email protected]: Sympy can't do elementary integration of type quadratic * sqrt(quadratic)
http://code.google.com/p/sympy/issues/detail?id=2477

In current master,


In [10]: f = (x**2 + 3*x + 1)*((x**2 + 10*x +101)**(1/2))

In [11]: f
Out[11]:
                  ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎛ 2          ⎞   ╱  2
⎝x  + 3⋅x + 1⎠⋅╲╱  x  + 10⋅x + 101

In [12]: f.integrate(x)
Out[12]:
⌠
⎮                   ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎮ ⎛ 2          ⎞   ╱  2
⎮ ⎝x  + 3⋅x + 1⎠⋅╲╱  x  + 10⋅x + 101  dx
⌡

In [13]: f.integrate(x).doit()
Out[13]:
⌠
⎮                   ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎮ ⎛ 2          ⎞   ╱  2
⎮ ⎝x  + 3⋅x + 1⎠⋅╲╱  x  + 10⋅x + 101  dx
⌡

In [18]: f.integrate((x, 0, 1))
Out[18]:
1
⌠
⎮                   ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎮ ⎛ 2          ⎞   ╱  2
⎮ ⎝x  + 3⋅x + 1⎠⋅╲╱  x  + 10⋅x + 101  dx
⌡
0

Is this integral possible with sympy ?

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