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

Given Integral: We are given the integral of a polynomial function: ∫(2x^2 + 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 2x^2: First, we integrate the term 2x^2: ∫2x^2 dx = 2 * ∫x^2 dx = 2 * (x^(2+1)/(2+1)) = 2 * (x^3/3) = (2/3)x^3 There is no math error in this step.Integrating 5x^5: Next, we integrate the term 5x^5: ∫5x^5 dx = 5 * ∫x^5 dx = 5 * (x^(5+1)/(5+1)) = 5 * (x^6/6) = (5/6)x^6 Again, there is no math error in this step.Combining Results: Now, we combine the results of the two integrals: ∫(2x^2 + 5x^5)dx = (2/3)x^3 + (5/6)x^6 We add the constant of integration, C, to represent the indefinite integral: (2/3)x^3 + (5/6)x^6 + C There is no math error in this step.

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Calculate the integral and write the answer in simplest form.

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

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

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Calculus

Find indefinite integrals using the substitution

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

\newline

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

\newline

Answer:

Given Integral: We are given the integral of a polynomial function: $\int(2x^2 + 5x^5)\,dx$ 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 $2x^2$ : First, we integrate the term $2x^2$ :
$\int 2x^2 dx = 2 \times \int x^2 dx = 2 \times \left(\frac{x^{2+1}}{2+1}\right) = 2 \times \left(\frac{x^3}{3}\right) = \frac{2}{3}x^3$
There is no math error in this step.
Integrating $5x^5$ : Next, we integrate the term $5x^5$ :
$\int 5x^5 dx = 5 \times \int x^5 dx = 5 \times (x^{5+1}/(5+1)) = 5 \times (x^6/6) = (5/6)x^6$
Again, there is no math error in this step.
Combining Results: Now, we combine the results of the two integrals: $\newline$ $\int(2x^2 + 5x^5)dx = \frac{2}{3}x^3 + \frac{5}{6}x^6$ $\newline$ We add the constant of integration, $C$ , to represent the indefinite integral: $\newline$ $\frac{2}{3}x^3 + \frac{5}{6}x^6 + C$ $\newline$ There is no math error in this step.