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

Integrate -x: We are given the integral of the function -x + 2x^5. We will integrate each term separately. The integral of -x with respect to x is -x^2/2. The integral of 2x^5 with respect to x is 2x^6/6 or x^6/3.Integrate 2x^5: Now we combine the results of the two integrals. The combined integral is -x^2/2 + x^6/3 + C, where C is the constant of integration.Combine integrals: We check for any mathematical errors in the integration process. The integration was performed correctly, and the powers of x were increased by one and divided by the new exponent, as per the power rule of integration.

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Find indefinite integrals using the substitution

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

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

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Answer:

Integrate $-x$ : We are given the integral of the function $-x + 2x^5$ . We will integrate each term separately. $\newline$ The integral of $-x$ with respect to $x$ is $-\frac{x^2}{2}$ . $\newline$ The integral of $2x^5$ with respect to $x$ is $\frac{2x^6}{6}$ or $\frac{x^6}{3}$ .
Integrate $2x^5$ : Now we combine the results of the two integrals. $\newline$ The combined integral is $-\frac{x^2}{2} + \frac{x^6}{3} + C$ , where $C$ is the constant of integration.
Combine integrals: We check for any mathematical errors in the integration process. The integration was performed correctly, and the powers of $x$ were increased by one and divided by the new exponent, as per the power rule of integration.