Evaluate the integral and express your answer in simplest form. int(4)/(sqrt(1-x^(2)))dx Answer:

Given Integral: We are given the integral: int(4)/(sqrt(1-x^(2)))dx This integral is a standard form that resembles the integral of the derivative of arcsine, which is: int(1)/(sqrt(1-x^(2)))dx = arcsin(x) + C To solve the given integral, we can factor out the constant 4 from the integral: int(4)/(sqrt(1-x^(2)))dx = 4 * int(1)/(sqrt(1-x^(2)))dxFactor Out Constant: Now we can integrate using the standard form: 4 * int(1)/(sqrt(1-x^(2)))dx = 4 * arcsin(x) + C where C is the constant of integration.Integrate Using Standard Form: Therefore, the integral evaluates to: 4 * arcsin(x) + C This is the simplest form of the answer.

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Find indefinite integrals using the substitution

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Q. Evaluate the integral and express your answer in simplest form.

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\int \frac{4}{\sqrt{1-x^{2}}} d x

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Answer:

Given Integral: We are given the integral: $\newline$ $\int\frac{4}{\sqrt{1-x^{2}}}dx$ $\newline$ This integral is a standard form that resembles the integral of the derivative of arcsine, which is: $\newline$ $\int\frac{1}{\sqrt{1-x^{2}}}dx = \arcsin(x) + C$ $\newline$ To solve the given integral, we can factor out the constant $4$ from the integral: $\newline$ $\int\frac{4}{\sqrt{1-x^{2}}}dx = 4 \times \int\frac{1}{\sqrt{1-x^{2}}}dx$
Factor Out Constant: Now we can integrate using the standard form: $\newline$ $4 \cdot \int \frac{1}{\sqrt{1-x^{2}}} \, dx = 4 \cdot \arcsin(x) + C$ $\newline$ where $C$ is the constant of integration.
Integrate Using Standard Form: Therefore, the integral evaluates to: $\newline$ $4 \cdot \arcsin(x) + C$ $\newline$ This is the simplest form of the answer.