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

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

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integral of 2sec(x)tan(x)

\int 2 sec (x) tan (x) d x

2 sec (x) + C

Solution steps

\int 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

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

Apply u-substitution

: \int 1 d u

= 2 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot u

Substitute back

u = sec (x)

= 2 \cdot 1 \cdot sec (x)

Simplify

= 2 sec (x)

Add a constant to the solution

= 2 sec (x) + C

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

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

\int \frac{sin ( \frac{1}{x ^{6}} )}{x ^{7}} d x

\frac{d}{d x} (\frac{1}{2} cos^{2} (x))

f (x) = \frac{3}{x ^{\frac{1}{2}}}

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