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

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

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integral of tan^4(x)

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

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

Solution steps

\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

6 + \frac{2 t}{1 + t ^{3}} - e^{- 0.02 t}

\frac{d}{d s} (e^{- s})

\int 5 cos (\frac{x}{2}) d x

x^{2} 16 - x^{2}

\frac{1}{s ^{2} - 2 s}

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