Evaluate the integral. int-6xe^(-x)dx Answer:

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Evaluate the integral.  int-6xe^(-x)dx Answer:

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Set up integration by parts: Let's use integration by parts to evaluate the integral of -6xe^(-x) with respect to x. Integration by parts is given by the formula ∫u dv = uv - ∫v du, where u and dv are parts of the integrand that we choose. We will let u = -6x and dv = e^(-x)dx. Then we need to find du and v. Calculating du and v: du = -6 dx (derivative of -6x with respect to x) v = -e^(-x) (antiderivative of e^(-x) with respect to x)Calculate du and v: Now we apply the integration by parts formula: ∫-6xe^(-x)dx = uv - ∫v du Substituting the values of u, v, du, and dv we found: ∫-6xe^(-x)dx = (-6x)(-e^(-x)) - ∫(-e^(-x))(-6)dx Simplifying the expression: ∫-6xe^(-x)dx = 6xe^(-x) - ∫6e^(-x)dxApply integration by parts: Next, we integrate the remaining integral ∫6e^(-x)dx. The antiderivative of 6e^(-x) with respect to x is -6e^(-x), since the derivative of -6e^(-x) is 6e^(-x). So, ∫6e^(-x)dx = -6e^(-x) + C, where C is the constant of integration.Integrate remaining integral: Now we combine the results from the previous steps: ∫-6xe^(-x)dx = 6xe^(-x) - (-6e^(-x) + C) Simplifying the expression: ∫-6xe^(-x)dx = 6xe^(-x) + 6e^(-x) + C

Evaluate the integral. $\newline$ $\int-6 x e^{-x} d x$ $\newline$ Answer:

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