Calculate the integral and write the answer in simplest form. int(-2x+5x^(5))dx Answer:

Identify integral function: Identify the integral to be solved. We need to integrate the function -2x + 5x^5 with respect to x.Apply power rule: Apply the power rule for integration to each term separately. The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. For the first term, -2x, we have n = 1, so the integral is -2 * (x^(1+1))/(1+1). For the second term, 5x^5, we have n = 5, so the integral is 5 * (x^(5+1))/(5+1).Perform integration: Perform the integration for each term. For the first term, -2x, the integral is -2 * (x^2)/2 = -x^2. For the second term, 5x^5, the integral is 5 * (x^6)/6 = (5/6)x^6.Combine results: Combine the results of the integrals and add the constant of integration. The combined integral is -x^2 + (5/6)x^6 + C, where C is the constant of integration.

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Calculate the integral and write the answer in simplest form.

int(-2x+5x^(5))dx
Answer:

Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(-2 x+5 x^{5}\right) d x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the power rule

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Q. Calculate the integral and write the answer in simplest form.

\newline

\int\left(-2 x+5 x^{5}\right) d x

\newline

Answer:

Identify integral function: Identify the integral to be solved. $\newline$ We need to integrate the function $-2x + 5x^5$ with respect to $x$ .
Apply power rule: Apply the power rule for integration to each term separately. $\newline$ The power rule for integration states that $\int x^n \, dx = \frac{x^{(n+1)}}{n+1} + C$ , where $C$ is the constant of integration. $\newline$ For the first term, $-2x$ , we have $n = 1$ , so the integral is $-2 \times \frac{x^{(1+1)}}{1+1}$ . $\newline$ For the second term, $5x^5$ , we have $n = 5$ , so the integral is $5 \times \frac{x^{(5+1)}}{5+1}$ .
Perform integration: Perform the integration for each term. $\newline$ For the first term, $-2x$ , the integral is $-2 \times (x^2)/2 = -x^2$ . $\newline$ For the second term, $5x^5$ , the integral is $5 \times (x^6)/6 = (5/6)x^6$ .
Combine results: Combine the results of the integrals and add the constant of integration. The combined integral is $-x^2 + \left(\frac{5}{6}\right)x^6 + C$ , where $C$ is the constant of integration.