What is the integral of 2tan^2(x)+tan^4(x) ?

The integral of 2tan^2(x)+tan^4(x) is -x+1/3 tan^3(x)+tan(x)+C

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integral of 2tan^2(x)+tan^4(x)

\int 2 tan^{2} (x) + tan^{4} (x) d x

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

Solution steps

\int 2 tan^{2} (x) + tan^{4} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 tan^{2} (x) d x + \int tan^{4} (x) d x

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

\int tan^{4} (x) d x = \frac{1}{3} tan^{3} (x) + x - tan (x)

= 2 (- x + tan (x)) + \frac{1}{3} tan^{3} (x) + x - tan (x)

Simplify

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

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

Add a constant to the solution

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

\int \frac{x}{3 x + 1} d x

\int \frac{tan ( θ )}{sec ( θ )} d θ

\int x cos (πn x) d x

x \to 0 lim (\frac{3 x ^{2}}{x ^{2}})

x \to 6 + lim (x - 6)

What is the integral of 2tan^2(x)+tan^4(x) ?
The integral of 2tan^2(x)+tan^4(x) is -x+1/3 tan^3(x)+tan(x)+C