What is the integral of sec(t)(sec(t)-tan(t)) ?

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

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integral of sec(t)(sec(t)-tan(t))

\int sec (t) (sec (t) - tan (t)) d t

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

Solution steps

\int sec (t) (sec (t) - tan (t)) d t

Apply u-substitution

: \int \frac{2}{( u + 1 ) ^{2}} d u

= \int \frac{2}{( u + 1 ) ^{2}} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{( u + 1 ) ^{2}} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= 2 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 2 (- \frac{1}{v})

Substitute back

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

Simplify

2 (- \frac{1}{tan ( \frac{t}{2} ) + 1}) : - \frac{2}{tan ( \frac{t}{2} ) + 1}

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{f ( x ) ( x ) ^{- 1} ( x )})

d s = 2 s d t

n = 0 \sum \infty 5 (- \frac{1}{3})^{n}

x \to 4 lim (\frac{( x ^{2} - 16 )}{2 - x})

\frac{d}{d x} (ln (2 e^{- x} sin (x)))

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