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

The integral of (sec^2(x))/(2tan(x)) is 1/2 ln|tan(x)|+C

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

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

\frac{1}{2} ln ∣ tan (x) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = tan (x)

= \frac{1}{2} ln ∣ tan (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (x) ∣ + C

x \to 6 lim (\frac{x ^{6}}{( x - 6 )})

\frac{\partial}{\partial x} (\frac{x}{x})

\int \frac{1}{3 sin ( x ) - 4 cos ( x )} d x

x y^{^{'}} + 3 y = 1984 x^{1982}

\int \frac{1}{[ ( a x ) ^{2} - b ^{2} ] ^{\frac{3}{2}}} d x

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