Mathematics

Problem

Which of the following statements is always true for differentiable functions

f

and

g

and real constants

a

and

b

? a)

\displaystyle \int \bigl(af(x)+bg(x)\bigr)\,dx = a\int f(x)\,dx + b\int g(x)\,dx

\displaystyle \int \frac{f(x)}{g(x)}\,dx = \frac{\int f(x)\,dx}{\int g(x)\,dx} + C

\displaystyle \int \left(af(x)+bg(x)\right)\,dx = a\int f(x)\,dx + b\int g(x)\,dx + C

\displaystyle \int \bigl(f(x)g(x)\bigr)\,dx = \int f(x)\,dx\; \int g(x)\,dx + C