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

Rewrite integral: Rewrite the integral in a more convenient form for integration. The integral of (3sqrt(x^(5)))/(2) can be rewritten by expressing the square root as a power of 1/2. I = ∫(3/2)x^(5/2) dxApply power rule: Apply the power rule for integration. The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. I = (3/2) ∫x^(5/2) dx I = (3/2) * [(x^(5/2 + 1))/(5/2 + 1)] + CSimplify expression: Simplify the expression. Now we simplify the exponent and the fraction. I = (3/2) * [(x^(7/2))/(7/2)] + C I = (3/2) * (2/7) * x^(7/2) + C I = (3/7) * x^(7/2) + CFinal answer: Write the final answer in simplest form. The integral in simplest form is: I = (3/7)x^(7/2) + C

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Calculate the integral and write your answer in simplest form.

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

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

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Calculus

Find indefinite integrals using the substitution and by parts

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

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

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Answer:

Rewrite integral: Rewrite the integral in a more convenient form for integration. $\newline$ The integral of $(3\sqrt{x^{5}})/(2)$ can be rewritten by expressing the square root as a power of $1/2$ . $\newline$ $I = \int(\frac{3}{2})x^{\frac{5}{2}} \, dx$
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. $\newline$ $I = \frac{3}{2} \int x^{\frac{5}{2}} \, dx$ $\newline$ $I = \frac{3}{2} \cdot \left[\frac{x^{\frac{5}{2} + 1}}{\frac{5}{2} + 1}\right] + C$
Simplify expression: Simplify the expression. $\newline$ Now we simplify the exponent and the fraction. $\newline$ $I = \frac{3}{2} \times \left[\frac{x^{\frac{7}{2}}}{\frac{7}{2}}\right] + C$ $\newline$ $I = \frac{3}{2} \times \frac{2}{7} \times x^{\frac{7}{2}} + C$ $\newline$ $I = \frac{3}{7} \times x^{\frac{7}{2}} + C$
Final answer: Write the final answer in simplest form. $\newline$ The integral in simplest form is: $\newline$ $I = \frac{3}{7}x^{\frac{7}{2}} + C$