Calculate the integral and write the answer in simplest form. int(6+2x^(-2)-2x)dx Answer:

Given integral: We are given the integral to solve: int(6 + 2x^(-2) - 2x)dx We will integrate each term separately.Integrate constant term: First, integrate the constant term 6 with respect to x: int(6)dx = 6xIntegrate term 2x^(-2): Next, integrate the term 2x^(-2) with respect to x: int(2x^(-2))dx = 2 * int(x^(-2))dx = 2 * (-x^(-1)) = -2/xIntegrate term -2x: Finally, integrate the term -2x with respect to x: int(-2x)dx = -2 * int(x)dx = -2 * (x^2/2) = -x^2Combine integrated terms: Combine all the integrated terms and add the constant of integration C: 6x - 2/x - x^2 + C

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Calculus

Find indefinite integrals using the substitution

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

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\int\left(6+2 x^{-2}-2 x\right) d x

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Answer:

Given integral: We are given the integral to solve: $\newline$ $\int(6 + 2x^{-2} - 2x)\,dx$ $\newline$ We will integrate each term separately.
Integrate constant term: First, integrate the constant term $6$ with respect to $x$ : $\int(6)\,dx = 6x$
Integrate term $2x^{-2}$ : Next, integrate the term $2x^{-2}$ with respect to $x$ : $\newline$ $\int(2x^{-2})dx = 2 \cdot \int(x^{-2})dx = 2 \cdot (-x^{-1}) = -\frac{2}{x}$
Integrate term $-2x$ : Finally, integrate the term $-2x$ with respect to $x$ : $\int(-2x)\,dx = -2 \times \int(x)\,dx = -2 \times \left(\frac{x^2}{2}\right) = -x^2$
Combine integrated terms: Combine all the integrated terms and add the constant of integration $C$ : $6x - \frac{2}{x} - x^2 + C$