What is the integral of tan^4(θ) ?

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

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integral of tan^4(θ)

\int tan^{4} (θ) d θ

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

Solution steps

\int tan^{4} (θ) d θ

Apply Integral Reduction

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

\int tan^{2} (θ) d θ = - θ + tan (θ)

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{( x ^{2} + x + 1 )}{( 2 x + 1 ) ( x ^{2} + 1 )} d x

\int 7 x - 3 d x

\int (sin (x) 1 + cos (x)) d x

\frac{d}{d x} (ln (sec^{3} (x^{4} - 1)))

x^{3}

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