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

\int (π x^{3} + 1)^{4} 3 π x^{2} d x

\frac{\partial}{\partial x} (10 - x^{2} - y^{2})

\frac{\partial}{\partial x} (ln (8 - x e^{- x}))

\frac{d}{d x} ((\frac{4 x ^{2}}{8 - x})^{3})

x \to 1 lim (\frac{x ^{3} + 1}{x - 1})

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