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Mathematics, 18.01.2021 21:30 ZachDom4784

Find the indefinit integral x^3-1/x^2 dx

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Answer from: johannah51

$\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \frac{x^2}{2} + \frac{1}{x} + C$

General Formulas and Concepts:

Algebra I

Exponential Property [Dividing]: $\displaystyle \frac{b^m}{b^n} = b^{m - n}$ Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Integration

Integrals[Indefinite Integrals] integration Constant C

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

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

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx$

Step 2: Integrate

[Integrand] Rewrite: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \int {\bigg( \frac{x^3}{x^2} - \frac{1}{x^2} \bigg)} \, dx$ Simplify [Exponential Property - Dividing]: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \int {\bigg( x - \frac{1}{x^2} \bigg)} \, dx$ [Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \int {x} \, dx - \int {\frac{1}{x^2}} \, dx$ [2nd Integral] Rewrite [Exponential Property - Rewrite]: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \int {x} \, dx - \int {x^{-2}} \, dx$ [Integrals] Reverse Power Rule: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \frac{x^2}{2} - (-x^{-1}) + C$ Simplify/Rewrite [Exponential Property - Rewrite]: $\displaystyle \int {\frac{x^3 - 1}{x^2}} \, dx = \frac{x^2}{2} + \frac{1}{x} + C$

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

Unit: Integration

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Answer from: Quest

The answer is d. 606 because you have to multiply 30% ( percent) times 2020 (total) to get ur answer.

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Answer from: Quest

step-by-step explanation:

which of the following statements correctly describes the expression below based on its degree and number of terms?

314 - 7x2 + 11

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