Mathematics, 02.09.2020 04:01 oliviabob9893

Find the following integral.
Integrate x + 5/x^2 +10x +26 dx

Answers: 3

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Answers

Answer from: HahaHELPP

$\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

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

IntegralsDefinite/Indefinite IntegralsIntegration Constant C

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

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

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx$

Step 2: Integrate Pt. 1

Set variables for u-substitution.

Set u: $\displaystyle u = x^2 + 10x + 26$ [u] Differentiate [Addition/Subtraction, Basic Power Rule]: $\displaystyle du = 2x + 10 \ dx$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2(x + 5)}{x^2 + 10x + 26}} \, dx$ [Integrand] Expand: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2x + 10}{x^2 + 10x + 26}} \, dx$ [Integral] U-Substitution: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{1}{u}} \, du$ [Integral] Logarithmic Integration: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|u| + C$ Back-Substitute: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|x^2 + 10x + 26| + C$ Simplify: $\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C$

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

Unit: Integration

Answer from: Quest

24: 56

step-by-step explanation:

24 can be divided into 3 and 56 can be divided into 7, where as all the other ratios can't.

Answer from: Quest

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation:

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Find the following integral.
Integrate x + 5/x^2 +10x +26 dx...