What is the integral of 3cot^4(x) ?

The integral of 3cot^4(x) is -cot^3(x)+3x+3cot(x)+C

Popular >

integral of 3cot^4(x)

\int 3 cot^{4} (x) d x

- cot^{3} (x) + 3 x + 3 cot (x) + C

Solution steps

\int 3 cot^{4} (x) d x

Take the constant out:

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

= 3 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

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

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

= 3 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

3 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : - cot^{3} (x) + 3 x + 3 cot (x)

= - cot^{3} (x) + 3 x + 3 cot (x)

Add a constant to the solution

= - cot^{3} (x) + 3 x + 3 cot (x) + C

\frac{d}{d x} (5 x - 1)

f (x) = x^{2} - 3 x, at x = 1

\int (12 - 3 t^{2}) d t

\frac{2 s}{( s + 3 ) ^{2} + 7}

x \to - 2 lim ((x + 1) \cdot (x + 1))

What is the integral of 3cot^4(x) ?
The integral of 3cot^4(x) is -cot^3(x)+3x+3cot(x)+C