Evaluate the integral. int((5)/(x^(5))-9x^(5))dx Answer:

Given Integral: We are given the integral to evaluate: ∫((5/x^5) - 9x^5)dx We can split this integral into two separate integrals: ∫(5/x^5)dx - ∫(9x^5)dx Now we will integrate each term separately.Split into Two: First, let's integrate ∫(5/x^5)dx. This is the same as ∫5x^(-5)dx. To integrate x^n, we use the power rule for integration, which states that ∫x^n dx = x^(n+1)/(n+1) + C, where n ≠ -1. Applying this rule, we get: ∫5x^(-5)dx = 5 * x^(-5+1)/(-5+1) + C = 5 * x^(-4)/(-4) + C = -5/4 * x^(-4) + CIntegrate 5/x^5: Next, we integrate ∫(9x^5)dx. Again, using the power rule for integration: ∫9x^5 dx = 9 * x^(5+1)/(5+1) + C = 9 * x^6/6 + C = 3/2 * x^6 + CIntegrate 9x^5: Now we combine the results of the two integrals: -5/4 * x^(-4) + 3/2 * x^6 + C This is the antiderivative of the given function.Combine Results: We can write the final answer as: -5/4 * x^(-4) + 3/2 * x^6 + C

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Evaluate the integral.

int((5)/(x^(5))-9x^(5))dx
Answer:

Evaluate the integral. $\newline$ $\int\left(\frac{5}{x^{5}}-9 x^{5}\right) \mathrm{d} x$ $\newline$ Answer:

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Calculus

Find indefinite integrals using the substitution

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Q. Evaluate the integral.

\newline

\int\left(\frac{5}{x^{5}}-9 x^{5}\right) \mathrm{d} x

\newline

Answer:

Given Integral: We are given the integral to evaluate: $\newline$ $\int((\frac{5}{x^5}) - 9x^5)dx$ $\newline$ We can split this integral into two separate integrals: $\newline$ $\int(\frac{5}{x^5})dx - \int(9x^5)dx$ $\newline$ Now we will integrate each term separately.
Split into Two: First, let's integrate $\int(\frac{5}{x^5})dx$ . This is the same as $\int 5x^{-5}dx$ . To integrate $x^n$ , we use the power rule for integration, which states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ , where $n \neq -1$ . Applying this rule, we get: $\int 5x^{-5}dx = 5 * \frac{x^{-5+1}}{-5+1} + C = 5 * \frac{x^{-4}}{-4} + C = -\frac{5}{4} * x^{-4} + C$
Integrate $\frac{5}{x^5}$ : Next, we integrate $\int(9x^5)dx$ . $\newline$ Again, using the power rule for integration: $\newline$ $\int 9x^5 dx = 9 \cdot \frac{x^{5+1}}{5+1} + C$ $\newline$ $= 9 \cdot \frac{x^6}{6} + C$ $\newline$ $= \frac{3}{2} \cdot x^6 + C$
Integrate $9x^5$ : Now we combine the results of the two integrals: $\newline$ $-\frac{5}{4} * x^{-4} + \frac{3}{2} * x^6 + C$ $\newline$ This is the antiderivative of the given function.
Combine Results: We can write the final answer as: $-\frac{5}{4} \cdot x^{-4} + \frac{3}{2} \cdot x^6 + C$