What is the integral of cot^4(1/2)t ?

The integral of cot^4(1/2)t is (cot^4(1/2)t^2)/2+C

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integral of cot^4(1/2)t

\int cot^{4} (\frac{1}{2}) t d t

\frac{cot ^{4} ( \frac{1}{2} ) t ^{2}}{2} + C

Solution steps

\int cot^{4} (\frac{1}{2}) t d t

Take the constant out:

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

= cot^{4} (\frac{1}{2}) \cdot \int t d t

Apply the Power Rule

: \frac{t ^{2}}{2}

= cot^{4} (\frac{1}{2}) \frac{t ^{2}}{2}

Multiply fractions:

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

= \frac{cot ^{4} ( \frac{1}{2} ) t ^{2}}{2}

Add a constant to the solution

= \frac{cot ^{4} ( \frac{1}{2} ) t ^{2}}{2} + C

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What is the integral of cot^4(1/2)t ?
The integral of cot^4(1/2)t is (cot^4(1/2)t^2)/2+C