What is the integral of (tan(x))^4 ?

The integral of (tan(x))^4 is 1/3 tan^3(x)+x-tan(x)+C

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integral of (tan(x))^4

\int (tan (x))^{4} d x

\frac{1}{3} tan^{3} (x) + x - tan (x) + C

Solution steps

\int (tan (x))^{4} d x

Rewrite using trig identities

= \int tan^{4} (x) d x

Apply Integral Reduction

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

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

= \frac{tan ^{3} ( x )}{3} - (- x + tan (x))

Simplify

\frac{tan ^{3} ( x )}{3} - (- x + tan (x)) : \frac{1}{3} tan^{3} (x) + x - tan (x)

= \frac{1}{3} tan^{3} (x) + x - tan (x)

Add a constant to the solution

= \frac{1}{3} tan^{3} (x) + x - tan (x) + C

\frac{d}{d x} (\frac{x ^{2} - 5 x + 4}{∣ x - 1 ∣})

\frac{d}{d x} (x^{1 - a})

\frac{\partial}{\partial x} (e^{\frac{y}{x}} \cdot y)

x \to 1 lim (\frac{e ^{x - 1} - 1}{ln ^{2} ( x )})

x^{2} - 4 x + 3, 3 + 4 x - x^{2}

What is the integral of (tan(x))^4 ?
The integral of (tan(x))^4 is 1/3 tan^3(x)+x-tan(x)+C