Calculate the integral and write the answer in simplest form. int(-6x^(5)-x)dx Answer:

Given Integral: We are given the integral of a polynomial function: int(-6x^(5)-x)dx To solve this, we will integrate each term separately.Integrating -6x^5: First, we integrate the term -6x^5 with respect to x. The power rule for integration states that the integral of x^n with respect to x is (x^(n+1))/(n+1), provided n is not equal to -1. So, the integral of -6x^5 is -6 * (x^(5+1))/(5+1).Integrating -x: Performing the calculation for the first term, we get: -6 * (x^6)/6 This simplifies to -x^6.Combining Integrals: Next, we integrate the term -x with respect to x. Again, using the power rule, the integral of x is (x^(1+1))/(1+1). So, the integral of -x is - (x^2)/2.Final Answer: Combining the results from the two integrals, we get the indefinite integral of the given function: - x^6 - (x^2)/2 + C where C is the constant of integration.We have now found the indefinite integral of the given function in its simplest form. The final answer is: - x^6 - (x^2)/2 + C

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Calculate the integral and write the answer in simplest form.

int(-6x^(5)-x)dx
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Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(-6 x^{5}-x\right) d x$ $\newline$ Answer:

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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.

\newline

\int\left(-6 x^{5}-x\right) d x

\newline

Answer:

Given Integral: We are given the integral of a polynomial function: $\int(-6x^{5}-x)dx$ To solve this, we will integrate each term separately.
Integrating $-6x^5$ : First, we integrate the term $-6x^5$ with respect to $x$ . The power rule for integration states that the integral of $x^n$ with respect to $x$ is $(x^{(n+1)})/(n+1)$ , provided $n$ is not equal to $-1$ . $\newline$ So, the integral of $-6x^5$ is $-6 \times (x^{(5+1)})/(5+1)$ .
Integrating $-x$ : Performing the calculation for the first term, we get: $\newline$ $-6 \times (x^6)/6$ $\newline$ This simplifies to $-x^6$ .
Combining Integrals: Next, we integrate the term $-x$ with respect to $x$ . Again, using the power rule, the integral of $x$ is $(x^{1+1})/(1+1)$ . So, the integral of $-x$ is $- (x^2)/2$ .
Final Answer: Combining the results from the two integrals, we get the indefinite integral of the given function: $\newline$ $- x^6 - \frac{x^2}{2} + C$ $\newline$ where $C$ is the constant of integration.
Final Answer: Combining the results from the two integrals, we get the indefinite integral of the given function: $\newline$ $- x^6 - \frac{x^2}{2} + C$ $\newline$ where $C$ is the constant of integration.We have now found the indefinite integral of the given function in its simplest form. $\newline$ The final answer is: $\newline$ $- x^6 - \frac{x^2}{2} + C$