Sum Rule

Reference > Calculus: Integration

Description
∫f(x)+g(x) dx=∫f(x) dx+∫g(x) dx\int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx
Examples
∫cos⁡x+sin⁡x dx\int \cos{x}+\sin{x} \, dx
1
Use Sum Rule: ∫f(x)+g(x) dx=∫f(x) dx+∫g(x) dx\int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx.
∫cos⁡x dx+∫sin⁡x dx\int \cos{x} \, dx+\int \sin{x} \, dx

2
Use Trigonometric Integration: the integral of cos⁡x\cos{x} is sin⁡x\sin{x}.
sin⁡x+∫sin⁡x dx\sin{x}+\int \sin{x} \, dx

3
Use Trigonometric Integration: the integral of sin⁡x\sin{x} is −cos⁡x-\cos{x}.
sin⁡x−cos⁡x\sin{x}-\cos{x}

4
Add constant.
sin⁡x−cos⁡x+C\sin{x}-\cos{x}+C

Done

See Also

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