Mathematics, 14.01.2020 20:31, 2020seogang

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

Answers: 3

Show answers

Answers

answered: 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

answered: Guest

answer: no

step-by-step explanation:

answered: Guest

the first one, all those points on the line just make a strait line.

Which table represents a linear function?

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:20, amortegaa805

Which best explains why this triangle is or is not a right triangle?

Answers: 1

continue

Mathematics, 21.06.2019 16:20, kingalex7575

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Answers: 1

continue

Mathematics, 21.06.2019 18:30, luvme68297

Which statement justifies why angle ebc measures 90?

Answers: 3

continue

Mathematics, 22.06.2019 00:30, reneewilliams20

Find the solution on the interval [0, 2pi)

Answers: 3

continue

Do you know the correct answer?

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