What is the integral of (1/2 sec(x)tan(x)) ?

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

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integral of (1/2 sec(x)tan(x))

\int (\frac{1}{2} sec (x) tan (x)) d x

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

Solution steps

\int \frac{1}{2} sec (x) 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 sec (x) tan (x) d x

Apply u-substitution

: \int 1 d u

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

Integral of a constant:

\int a d x = a x

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

Substitute back

u = sec (x)

= \frac{1}{2} \cdot 1 \cdot sec (x)

Simplify

= \frac{1}{2} sec (x)

Add a constant to the solution

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

x \to 0 lim (\frac{x}{x + 3})

\int_{1}^{2} 3 ln (4 x) d x

\int - 3 x^{- 2} d x

f (x) = (2 x^{3} + 1)^{2}, (- 1, 1)

x \to 0 lim (\frac{( e e ^{- a x} - e ^{- b x} )}{x})

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