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

Write Integral: Write down the integral to be solved. I = ∫(-x^(-3) - 6)dxSplit Integral: Split the integral into two separate integrals. I = ∫(-x^(-3))dx - ∫(6)dxIntegrate First Term: Integrate the first term ∫(-x^(-3))dx. I₁ = ∫(-x^(-3))dx = -∫(x^(-3))dx = -1/2 * x^(-2) = -1/(2x^2)Integrate Second Term: Integrate the second term ∫(6)dx. I₂ = ∫(6)dx = 6xCombine Results: Combine the results of the two integrals and add the constant of integration C. I = I₁ + I₂ + C I = -1/(2x^2) + 6x + CFinal Answer: Write the final answer in simplest form. The indefinite integral of the function -x^(-3) - 6 with respect to x is -1/(2x^2) + 6x + C.

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Find indefinite integrals using the substitution and by parts

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Q. Calculate the integral and write the answer in simplest form.

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\int\left(-x^{-3}-6\right) d x

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Answer:

Write Integral: Write down the integral to be solved. $\newline$ $I = \int(-x^{-3} - 6)\,dx$
Split Integral: Split the integral into two separate integrals. $I = \int(-x^{-3})\,dx - \int(6)\,dx$
Integrate First Term: Integrate the first term $\int(-x^{-3})\,dx$ . $I_1 = \int(-x^{-3})\,dx = -\int(x^{-3})\,dx = -\frac{1}{2} \cdot x^{-2} = -\frac{1}{2x^2}$
Integrate Second Term: Integrate the second term $\int(6)\,dx$ . $I_2 = \int(6)\,dx = 6x$
Combine Results: Combine the results of the two integrals and add the constant of integration $C$ . $I = I_1 + I_2 + C$ $I = -\frac{1}{2x^2} + 6x + C$
Final Answer: Write the final answer in simplest form. $\newline$ The indefinite integral of the function $-x^{-3} - 6$ with respect to $x$ is $-\frac{1}{2x^2} + 6x + C$ .