Calculate the integral and write the answer in simplest form. int(3+6x^(-3))dx Answer:

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Calculate the integral and write the answer in simplest form.  int(3+6x^(-3))dx Answer:

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Identify integral: Identify the integral to be solved. We need to find the indefinite integral of the function 3 + 6x^(-3) with respect to x. The integral is written as ∫(3 + 6x^(-3))dx.Break down parts: Break down the integral into simpler parts. The integral of a sum is the sum of the integrals, so we can write: ∫(3 + 6x^(-3))dx = ∫3dx + ∫6x^(-3)dx.Integrate constant: Integrate the constant term. The integral of a constant 3 with respect to x is 3x. So, ∫3dx = 3x.Integrate term: Integrate the term 6x^(-3). The integral of 6x^(-3) with respect to x is 6 times the integral of x^(-3) with respect to x. Using the power rule for integration, ∫x^n dx = x^(n+1)/(n+1) for n ≠ -1, we get: ∫6x^(-3)dx = 6 * (x^(-3+1)/(-3+1)) = 6 * (x^(-2)/(-2)) = -3x^(-2).Combine and add: Combine the results and add the constant of integration. Combining the results from steps 3 and 4, we get: ∫(3 + 6x^(-3))dx = 3x - 3x^(-2) + C.Simplify result: Simplify the result. The integral in its simplest form is: 3x - 3/x^2 + C.

Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(3+6 x^{-3}\right) d x$ $\newline$ Answer:

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Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(3+6 x^{-3}\right) d x$ $\newline$ Answer: