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

Simplify integrand: Simplify the integrand. The integral of a constant times a function is the constant times the integral of the function. So, we can take the constant 5/4 out of the integral. I = int(5sqrt(x^(3)))/(4)dx I = (5/4) * int(sqrt(x^(3)))dxRewrite square root: Rewrite the square root of x^3 as x^(3/2). I = (5/4) * int(sqrt(x^(3)))dx I = (5/4) * int(x^(3/2))dxApply power rule: Apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), provided n is not equal to -1. I = (5/4) * int(x^(3/2))dx I = (5/4) * [(x^(3/2 + 1))/(3/2 + 1)] + CSimplify exponent and fraction: Simplify the exponent and the fraction. I = (5/4) * [(x^(5/2))/(5/2)] + C I = (5/4) * [2/5 * x^(5/2)] + CSimplify constants: Simplify the constants. I = (5/4) * (2/5) * x^(5/2) + C I = (1/2) * x^(5/2) + CWrite final answer: Write the final answer. The indefinite integral of (5sqrt(x^(3)))/(4) with respect to x is (1/2) * x^(5/2) + C.

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Calculate the integral and write your answer in simplest form.

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

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

\newline

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

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Answer:

Simplify integrand: Simplify the integrand. $\newline$ The integral of a constant times a function is the constant times the integral of the function. So, we can take the constant $\frac{5}{4}$ out of the integral. $\newline$ $I = \int \frac{5\sqrt{x^{3}}}{4}dx$ $\newline$ $I = \left(\frac{5}{4}\right) \times \int \sqrt{x^{3}}dx$
Rewrite square root: Rewrite the square root of $x^3$ as $x^{(3/2)}$ . $\newline$ $I = \frac{5}{4} \int \sqrt{x^{3}}\,dx$ $\newline$ $I = \frac{5}{4} \int x^{(3/2)}\,dx$
Apply power rule: Apply the power rule for integration. $\newline$ The power rule states that the integral of $x^n$ with respect to $x$ is $(x^{(n+1)})/(n+1)$ , provided $n \neq -1$ . $\newline$ $I = \frac{5}{4} \int x^{\frac{3}{2}}\,dx$ $\newline$ $I = \frac{5}{4} \left[\frac{x^{(\frac{3}{2} + 1)}}{(\frac{3}{2} + 1)}\right] + C$
Simplify exponent and fraction: Simplify the exponent and the fraction. $\newline$ $I = \frac{5}{4} \cdot \left[\frac{x^{\frac{5}{2}}}{\frac{5}{2}}\right] + C$ $\newline$ $I = \frac{5}{4} \cdot \left[\frac{2}{5} \cdot x^{\frac{5}{2}}\right] + C$
Simplify constants: Simplify the constants. $\newline$ $I = \left(\frac{5}{4}\right) \cdot \left(\frac{2}{5}\right) \cdot x^{\frac{5}{2}} + C$ $\newline$ $I = \left(\frac{1}{2}\right) \cdot x^{\frac{5}{2}} + C$
Write final answer: Write the final answer. $\newline$ The indefinite integral of $\frac{5\sqrt{x^{3}}}{4}$ with respect to $x$ is $\frac{1}{2} \cdot x^{\frac{5}{2}} + C$ .