What is the integral of xcot^2(2)x^2 ?

The integral of xcot^2(2)x^2 is (cot^2(2)x^4)/4+C

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integral of xcot^2(2)x^2

\int x cot^{2} (2) x^{2} d x

\frac{cot ^{2} ( 2 ) x ^{4}}{4} + C

Solution steps

\int x cot^{2} (2) x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cot^{2} (2) \cdot \int x x^{2} d x

Simplify

x x^{2} : x^{3}

= cot^{2} (2) \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= cot^{2} (2) \frac{x ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cot ^{2} ( 2 ) x ^{4}}{4}

Add a constant to the solution

= \frac{cot ^{2} ( 2 ) x ^{4}}{4} + C

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What is the integral of xcot^2(2)x^2 ?
The integral of xcot^2(2)x^2 is (cot^2(2)x^4)/4+C