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

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

Popular >

integral of sec(θ/2)tan(θ/2)

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

2 sec (\frac{θ}{2}) + C

Solution steps

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

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{θ}{2})

Simplify

= 2 sec (\frac{θ}{2})

Add a constant to the solution

= 2 sec (\frac{θ}{2}) + C

\int \frac{6}{( 2 - x ) x ^{2} - 4 x + 3} d x

\int \frac{( 3 x + 1 )}{x ^{2}} d x

\int \frac{8}{x ^{2} x ^{2} - 16} d x

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

\int (2 x + 7)^{4} d x

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