Solve \int{ }^{ }x^{\frac{1}{3}}\cdot\left(1 x^{\frac

Question

Evaluate the integral

\frac{21}{32} x 21 x^{11} + C, C \in R

Evaluate

\int x^{\frac{1}{3}} (1 \times x^{\frac{4}{3}})^{\frac{1}{7}} d x

Any expression multiplied by 1 remains the same

\int x^{\frac{1}{3}} (x^{\frac{4}{3}})^{\frac{1}{7}} d x

Evaluate the power

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\int x^{\frac{1}{3}} \times x^{\frac{4}{21}} d x

Multiply the terms

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\int x^{\frac{11}{21}} d x

Use the property of integral \int x^{n} d x = \frac{x ^{n + 1}}{n + 1}

\frac{x ^{\frac{11}{21} + 1}}{\frac{11}{21} + 1}

Add the numbers

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\frac{x ^{\frac{32}{21}}}{\frac{11}{21} + 1}

Add the numbers

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\frac{x ^{\frac{32}{21}}}{\frac{32}{21}}

Multiply by the reciprocal

x^{\frac{32}{21}} \times \frac{21}{32}

Use the commutative property to reorder the terms

\frac{21}{32} x^{\frac{32}{21}}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

\frac{21}{32} 21 x^{32}

Simplify the radical expression

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\frac{21}{32} x 21 x^{11}

Solution

\frac{21}{32} x 21 x^{11} + C, C \in R

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