Integration of a function of a function

Hi, I report some results obtained by integrating a function of a function. In this case the result is correct,

import sympy as sy
t,x=sy.symbols('t x',real=True)
a=sy.Function('a', real=True)(t)
I=sy.Integral(a**2,a)
display(sy.Eq(I,I.doit()))
I=sy.Integral(x**2,x)
sy.Eq(I,I.doit())

$\displaystyle \int a^{2}{\left(t \right)}\, da{\left(t \right)} = \frac{a^{3}{\left(t \right)}}{3}$ $\displaystyle \int x^{2}\, dx = \frac{x^{3}}{3}$

in these others the results are wrong.

I=sy.Integral(sy.cos(a),a)              
display(sy.Eq(I,I.doit()))                
I=sy.Integral(sy.cos(x),x)              
sy.Eq(I,I.doit())

$\displaystyle \int \cos{\left(a{\left(t \right)} \right)}\, da{\left(t \right)} = a{\left(t \right)} \cos{\left(a{\left(t \right)} \right)}$ $\displaystyle \int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$

I=sy.Integral(1/a,a)
display(sy.Eq(I,I.doit()))                
I=sy.Integral(1/x,x)              
sy.Eq(I,I.doit())

$\displaystyle \int \frac{1}{a{\left(t \right)}}\, da{\left(t \right)} = 1$ $\displaystyle \int \frac{1}{x}\, dx = \log{\left(x \right)}$

I=sy.Integral(sy.ln(a),a)
display(sy.Eq(I,I.doit()))                
I=sy.Integral(sy.ln(x),x)              
sy.Eq(I,I.doit())

$\displaystyle \int \log{\left(a{\left(t \right)} \right)}\, da{\left(t \right)} = a{\left(t \right)} \log{\left(a{\left(t \right)} \right)}$ $\displaystyle \int \log{\left(x \right)}\, dx = x \log{\left(x \right)} - x$

sympy / sympy

Integration of a function of a function #22921