Calculate the integral and write the answer in simplest form. int(6x^(4)-6+5x^(5))dx Answer:

Given integral function: We are given the integral of a polynomial function: ∫(6x^4 - 6 + 5x^5)dx To solve this, we will integrate each term separately using the power rule for integration, which states that ∫x^n dx = x^(n+1)/(n+1) for any real number n ≠ -1.Integrating 6x^4: First, we integrate the term 6x^4: ∫6x^4 dx = 6 * ∫x^4 dx = 6 * (x^(4+1)/(4+1)) = 6 * (x^5/5)Integrating -6: Next, we integrate the constant term -6: ∫(-6) dx = -6 * ∫1 dx = -6xIntegrating 5x^5: Finally, we integrate the term 5x^5: ∫5x^5 dx = 5 * ∫x^5 dx = 5 * (x^(5+1)/(5+1)) = 5 * (x^6/6)Combining integrations: Now, we combine the results of the integrations and add the constant of integration C: ∫(6x^4 - 6 + 5x^5)dx = 6 * (x^5/5) - 6x + 5 * (x^6/6) + CSimplifying expression: We simplify the expression by multiplying the coefficients: (6/5)x^5 - 6x + (5/6)x^6 + CFinal answer: The final answer in simplest form is: (6/5)x^5 - 6x + (5/6)x^6 + C

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Calculate the integral and write the answer in simplest form.

int(6x^(4)-6+5x^(5))dx
Answer:

Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(6 x^{4}-6+5 x^{5}\right) d x$ $\newline$ Answer:

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

\newline

\int\left(6 x^{4}-6+5 x^{5}\right) d x

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Answer:

Given integral function: We are given the integral of a polynomial function: $\int(6x^4 - 6 + 5x^5)dx$ To solve this, we will integrate each term separately using the power rule for integration, which states that $\int x^n dx = \frac{x^{(n+1)}}{(n+1)}$ for any real number $n \neq -1$ .
Integrating $6x^4$ : First, we integrate the term $6x^4$ : $\int 6x^4 \, dx = 6 \times \int x^4 \, dx = 6 \times \left(\frac{x^{4+1}}{4+1}\right) = 6 \times \left(\frac{x^5}{5}\right)$
Integrating $-6$ : Next, we integrate the constant term $-6$ : $\newline$ $\int(-6) \, dx = -6 \times \int 1 \, dx = -6x$
Integrating $5x^5$ : Finally, we integrate the term $5x^5$ : $\int 5x^5 dx = 5 \times \int x^5 dx = 5 \times \left(\frac{x^{5+1}}{5+1}\right) = 5 \times \left(\frac{x^6}{6}\right)$
Combining integrations: Now, we combine the results of the integrations and add the constant of integration $C$ : $\int(6x^4 - 6 + 5x^5)\,dx = 6 \times \left(\frac{x^5}{5}\right) - 6x + 5 \times \left(\frac{x^6}{6}\right) + C$
Simplifying expression: We simplify the expression by multiplying the coefficients: $\frac{6}{5}x^5 - 6x + \frac{5}{6}x^6 + C$
Final answer: The final answer in simplest form is: $\frac{6}{5}x^5 - 6x + \frac{5}{6}x^6 + C$