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

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

Popular >

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

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

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

Solution steps

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

Rewrite using trig identities

= \int - 1 + sec^{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 1 d x + \int sec^{2} (x) d x + \int tan^{4} (x) d x

\int 1 d x = x

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

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

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

Simplify

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

Add a constant to the solution

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

n = 2 \sum \infty \frac{2}{3 ^{n}}

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

\frac{d y}{d t} - y = 1

\frac{d}{d x} (e^{2 x} ln (3 x))

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

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