What is the integral of 7tan^2(x)+tan^4(x) ?

The integral of 7tan^2(x)+tan^4(x) is -6x+1/3 tan^3(x)+6tan(x)+C

Popular >

integral of 7tan^2(x)+tan^4(x)

\int 7 tan^{2} (x) + tan^{4} (x) d x

- 6 x + \frac{1}{3} tan^{3} (x) + 6 tan (x) + C

Solution steps

\int 7 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 7 tan^{2} (x) d x + \int tan^{4} (x) d x

\int 7 tan^{2} (x) d x = 7 (- x + tan (x))

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

= 7 (- x + tan (x)) + \frac{1}{3} tan^{3} (x) + x - tan (x)

Simplify

7 (- x + tan (x)) + \frac{1}{3} tan^{3} (x) + x - tan (x) : - 6 x + \frac{1}{3} tan^{3} (x) + 6 tan (x)

= - 6 x + \frac{1}{3} tan^{3} (x) + 6 tan (x)

Add a constant to the solution

= - 6 x + \frac{1}{3} tan^{3} (x) + 6 tan (x) + C

\int 3 x^{3} - 5 x^{2} + 7 x + 2 d x

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

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

x \to 0 lim (\frac{1}{x + 1})

\int (\frac{1}{3}) x^{3} - 5 x d x

What is the integral of 7tan^2(x)+tan^4(x) ?
The integral of 7tan^2(x)+tan^4(x) is -6x+1/3 tan^3(x)+6tan(x)+C