Mathematics, 14.01.2020 20:31 2020seogang

Use integration by parts to find the integrals in exercise.
∫(x+6)ex dx.

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Answer from: Kookiexperfect9420

$\displaystyle \int {(x + 6)e^x} \, dx = (x + 5)e^x + C$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration by Parts: $\displaystyle \int {u} \, dv = uv - \int {v} \, du$

[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int {(x + 6)e^x} \, dx$

Step 2: Integrate Pt. 1

Identify variables for integration by parts using LIPET.

Set u: $\displaystyle u = x + 6$ [u] Basic Power Rule [Derivative Property - Addition/Subtraction]: $\displaystyle du = dx$ Set dv: $\displaystyle dv = e^x \ dx$ [dv] Exponential Integration: $\displaystyle v = e^x$

Step 3: Integrate Pt. 2

[Integral] Integration by Parts: $\displaystyle \int {(x + 6)e^x} \, dx = (x + 6)e^x - \int {e^x} \, dx$ [Integral] Exponential Integration: $\displaystyle \int {(x + 6)e^x} \, dx = (x + 6)e^x - e^x + C$ Factor: $\displaystyle \int {(x + 6)e^x} \, dx = e^x(x + 6 - 1) + C$ Simplify: $\displaystyle \int {(x + 6)e^x} \, dx = (x + 5)e^x + C$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer from: Quest

step-by-step explanation:

Answer from: Quest

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

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Use integration by parts to find the integrals in exercise.
∫(x+6)ex dx....

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