What is the integral of 8cot^4(t) ?

The integral of 8cot^4(t) is 8(-1/3 cot^3(t)+t+cot(t))+C

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integral of 8cot^4(t)

\int 8 cot^{4} (t) d t

8 (- \frac{1}{3} cot^{3} (t) + t + cot (t)) + C

Solution steps

\int 8 cot^{4} (t) d t

Take the constant out:

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

= 8 \cdot \int cot^{4} (t) d t

Apply Integral Reduction

= 8 (- \frac{cot ^{3} ( t )}{3} - \int cot^{2} (t) d t)

\int cot^{2} (t) d t = - t - cot (t)

= 8 (- \frac{cot ^{3} ( t )}{3} - (- t - cot (t)))

Simplify

8 (- \frac{cot ^{3} ( t )}{3} - (- t - cot (t))) : 8 (- \frac{1}{3} cot^{3} (t) + t + cot (t))

= 8 (- \frac{1}{3} cot^{3} (t) + t + cot (t))

Add a constant to the solution

= 8 (- \frac{1}{3} cot^{3} (t) + t + cot (t)) + C

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What is the integral of 8cot^4(t) ?
The integral of 8cot^4(t) is 8(-1/3 cot^3(t)+t+cot(t))+C