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Sum RuleDescription \[\int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx\] |
Examples \[\int \cos{x}+\sin{x} \, dx\] 1 Use 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 Use Trigonometric Integration: the integral of \(\cos{x}\) is \(\sin{x}\). \[\sin{x}+\int \sin{x} \, dx\] 3 Use Trigonometric Integration: the integral of \(\sin{x}\) is \(-\cos{x}\). \[\sin{x}-\cos{x}\] 4 Add constant. \[\sin{x}-\cos{x}+C\] Done  |
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