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

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

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integral of (tan^2(x))/2

integral

\frac{tan ^{2} ( x )}{2}

\frac{1}{2} (- x + tan (x)) + C

Solution steps

\int \frac{tan ^{2} ( x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int tan^{2} (x) d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int - 1 + sec^{2} (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

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

\int 1 d x = x

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

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

Add a constant to the solution

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

\frac{1}{( e ^{x} - 1 )}

x^{5} sin (x)

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

\frac{1}{( x ( x + 2 ) )}

5^{- x}

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