Calculate the integral and write your answer in simplest form. int(5root(4)(x^(3)))/(2)dx Answer:

Rewrite Integral: Rewrite the integral in a more familiar form. The given integral is $\int \frac{5\sqrt[4]{x^3}}{2} \, dx$. The fourth root of $x^3$ can be written as $x^{3/4}$, so the integral becomes $\int \frac{5x^{3/4}}{2} \, dx$.Simplify Coefficients: Simplify the constant coefficients. We can factor out the constant from the integral to simplify the expression. This gives us $\frac{5}{2} \int x^{3/4} \, dx$.Apply Power Rule: Apply the power rule for integration. The power rule states that $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$, where $C$ is the constant of integration. Applying this rule to our integral, we get $\frac{5}{2} \cdot \frac{x^{3/4 + 1}}{3/4 + 1} + C$.Simplify Exponent and Fraction: Simplify the exponent and the fraction. Adding $1$ to $3/4$ gives us $7/4$, so the integral becomes $\frac{5}{2} \cdot \frac{x^{7/4}}{7/4} + C$. To simplify the fraction, we multiply by the reciprocal of $7/4$, which is $4/7$.Multiply Constants: Multiply the constants and write the final answer. Multiplying $\frac{5}{2}$ by $4/7$ gives us $\frac{5 \cdot 4}{2 \cdot 7} = \frac{20}{14}$, which simplifies to $\frac{10}{7}$. Therefore, the final answer is $\frac{10}{7}x^{7/4} + C$.

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Calculate the integral and write your answer in simplest form.

int(5root(4)(x^(3)))/(2)dx
Answer:

Calculate the integral and write your answer in simplest form. $\newline$ $\int \frac{5 \sqrt[4]{x^{3}}}{2} \mathrm{dx}$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the power rule

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

\newline

\int \frac{5 \sqrt[4]{x^{3}}}{2} \mathrm{dx}

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Answer:

Rewrite Integral: Rewrite the integral in a more familiar form. $\newline$ The given integral is $\int \frac{5\sqrt[4]{x^3}}{2} \, dx$ . The fourth root of $x^3$ can be written as $x^{3/4}$ , so the integral becomes $\int \frac{5x^{3/4}}{2} \, dx$ .
Simplify Coefficients: Simplify the constant coefficients. $\newline$ We can factor out the constant from the integral to simplify the expression. This gives us $\frac{5}{2} \int x^{3/4} \, dx$ .
Apply Power Rule: Apply the power rule for integration. $\newline$ The power rule states that $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ , where $C$ is the constant of integration. Applying this rule to our integral, we get $\frac{5}{2} \cdot \frac{x^{3/4 + 1}}{3/4 + 1} + C$ .
Simplify Exponent and Fraction: Simplify the exponent and the fraction. $\newline$ Adding $1$ to $3/4$ gives us $7/4$ , so the integral becomes $\frac{5}{2} \cdot \frac{x^{7/4}}{7/4} + C$ . To simplify the fraction, we multiply by the reciprocal of $7/4$ , which is $4/7$ .
Multiply Constants: Multiply the constants and write the final answer. $\newline$ Multiplying $\frac{5}{2}$ by $4/7$ gives us $\frac{5 \cdot 4}{2 \cdot 7} = \frac{20}{14}$ , which simplifies to $\frac{10}{7}$ . Therefore, the final answer is $\frac{10}{7}x^{7/4} + C$ .