Sum Rule

Reference > Calculus: Integration

Description
\[\int f(x)+g(x) \,dx=\int f(x) \,dx+\int g(x) \,dx\]
Examples
\[\int \cos{x}+\sin{x} \,dx\]
1
Apply the Sum Rule: \(\int f(x)+g(x) \,dx=\int f(x) \,dx+\int g(x) \,dx\)
\[\int \cos{x} \,dx+\int \sin{x} \,dx\]

2
The integral of \(\cos{x}\) is \(\sin{x}\)
\[\sin{x}+\int \sin{x} \,dx\]

3
The integral of \(\sin{x}\) is \(-\cos{x}\)
\[\sin{x}-\cos{x}\]

4
Add constant
\[\sin{x}-\cos{x}+C\]

Done