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

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

Popular >

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

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

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

Solution steps

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

Apply u-substitution

: \int sec (u) tan (u) \cdot 2 d u

= \int sec (u) tan (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int sec (u) tan (u) d u

Apply u-substitution

: \int 1 d v

= 2 \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot v

Substitute back

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

Simplify

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

Add a constant to the solution

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

y = 2 5 - x^{2}

\int (x^{2} + 3)^{3} 2 x d x

\frac{\partial}{\partial x} (x^{5} y^{5})

\int \frac{v + 3}{v - 1} d v

\frac{d}{d x} (3 (5 - x)^{2})

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