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Integral (x pangkat 3 - cos x) dx

User Shimrit
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You can break the integral of a sum/difference into the sum/difference of the integrals:



\int (x^3-\cos(x))\;dx = \int x^3\; dx - \int \cos(x)\; dx


The first integral can be solved using the power rule for integrations:



\int x^n\; dx = (x^(n+1))/(n+1) \implies \int x^3\; dx = (x^4)/(4)


As for the second, remember the chain of derivation of trigonometric functions:



\sin(x) \to \cos(x) \to -\sin(x) \to -\cos(x) \to \sin(x) \ldots


The integration chain is the same, but it follows the opposite direction: the integral of the cosine function is the sine function. So, you have



- \int \cos(x)\; dx = -\sin(x)


Since this is an indefinite integral, we must add the generic costant to the answer:



(x^4)/(4) -\sin(x) + C

User Olejnjak
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