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

Simplify integrand: Simplify the integrand. The integrand (sqrt(x^(5)))/(4) can be simplified by expressing the square root of x^5 as x^(5/2). I = ∫(sqrt(x^(5)))/(4) dx I = ∫(x^(5/2))/(4) dxRewrite with constant outside: Rewrite the integral with the constant outside. Since the constant 1/4 does not depend on x, we can take it outside the integral. I = (1/4) ∫x^(5/2) dxApply power rule: Apply the power rule for integration. The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. I = (1/4) ∫x^(5/2) dx I = (1/4) * [(x^((5/2)+1))/((5/2)+1)] + CSimplify expression: Simplify the expression. Now we simplify the exponent and the fraction. I = (1/4) * [(x^(7/2))/(7/2)] + C I = (1/4) * [(2/7)x^(7/2)] + C I = (1/14)x^(7/2) + C

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Calculate the integral and write your answer in simplest form.

int(sqrt(x^(5)))/(4)dx
Answer:

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

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Find indefinite integrals using the substitution and by parts

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

\newline

\int \frac{\sqrt{x^{5}}}{4} \mathrm{dx}

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Answer:

Simplify integrand: Simplify the integrand. $\newline$ The integrand $\frac{\sqrt{x^{5}}}{4}$ can be simplified by expressing the square root of $x^5$ as $x^{\frac{5}{2}}$ . $\newline$ $I = \int \frac{\sqrt{x^{5}}}{4} dx$ $\newline$ $I = \int \frac{x^{\frac{5}{2}}}{4} dx$
Rewrite with constant outside: Rewrite the integral with the constant outside. $\newline$ Since the constant $\frac{1}{4}$ does not depend on $x$ , we can take it outside the integral. $\newline$ $I = \left(\frac{1}{4}\right) \int x^{\frac{5}{2}} \, dx$
Apply power rule: Apply the power rule for integration. $\newline$ The power rule for integration states that $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ , where $C$ is the constant of integration. $\newline$ $I = \frac{1}{4} \int x^{\frac{5}{2}} \, dx$ $\newline$ $I = \frac{1}{4} \cdot \left[\frac{x^{\left(\frac{5}{2}+1\right)}}{\left(\frac{5}{2}+1\right)}\right] + C$
Simplify expression: Simplify the expression. $\newline$ Now we simplify the exponent and the fraction. $\newline$ $I = \frac{1}{4} \cdot \left[\frac{x^{\frac{7}{2}}}{\frac{7}{2}}\right] + C$ $\newline$ $I = \frac{1}{4} \cdot \left[\frac{2}{7}x^{\frac{7}{2}}\right] + C$ $\newline$ $I = \frac{1}{14}x^{\frac{7}{2}} + C$