Calculate the integral and write the answer in simplest form. int(3x^(2)+6x^(4))dx Answer:

Integrate 3x^2: We are given the integral of a polynomial function. To solve this, we will integrate each term separately using the power rule for integration, which states that the integral of x^n with respect to x is (x^(n+1))/(n+1) for any real number n ≠ -1. Let's integrate the first term 3x^2: ∫3x^2 dx = 3 * ∫x^2 dx = 3 * (x^(2+1))/(2+1) = x^3Integrate 6x^4: Now, let's integrate the second term 6x^4: ∫6x^4 dx = 6 * ∫x^4 dx = 6 * (x^(4+1))/(4+1) = (6/5)x^5Combine integrals: Combine the results of the two integrals to get the final indefinite integral: ∫(3x^2 + 6x^4) dx = x^3 + (6/5)x^5 + C where C is the constant of integration.

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Calculate the integral and write the answer in simplest form.

int(3x^(2)+6x^(4))dx
Answer:

Calculate the integral and write the answer in simplest form. $\newline$ $\int\left(3 x^{2}+6 x^{4}\right) d x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the power rule

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

\newline

\int\left(3 x^{2}+6 x^{4}\right) d x

\newline

Answer:

Integrate $3x^2$ : We are given the integral of a polynomial function. To solve this, we will integrate each term separately using the power rule for integration, which states that the integral of $x^n$ with respect to $x$ is $\frac{x^{(n+1)}}{(n+1)}$ for any real number $n \neq -1$ . $\newline$ Let's integrate the first term $3x^2$ : $\newline$ $\int 3x^2 dx = 3 \times \int x^2 dx = 3 \times \frac{x^{(2+1)}}{(2+1)} = x^3$
Integrate $6x^4$ : Now, let's integrate the second term $6x^4$ : $\int 6x^4 dx = 6 \times \int x^4 dx = 6 \times \frac{x^{4+1}}{4+1} = \frac{6}{5}x^5$
Combine integrals: Combine the results of the two integrals to get the final indefinite integral: $\newline$ $\int(3x^2 + 6x^4) \, dx = x^3 + \frac{6}{5}x^5 + C$ $\newline$ where $C$ is the constant of integration.