What is the integral of sec((2x)/5)tan((2x)/5) ?

The integral of sec((2x)/5)tan((2x)/5) is 5/2 sec((2x)/5)+C

integral of sec((2x)/5)tan((2x)/5)

\int sec (\frac{2 x}{5}) tan (\frac{2 x}{5}) d x

\frac{5}{2} sec (\frac{2 x}{5}) + C

Solution steps

\int sec (\frac{2 x}{5}) tan (\frac{2 x}{5}) d x

Apply u-substitution

= \int sec (u) tan (u) \frac{5}{2} d u

Take the constant out:

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

= \frac{5}{2} \cdot \int sec (u) tan (u) d u

Apply u-substitution

= \frac{5}{2} \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= \frac{5}{2} \cdot 1 \cdot v

Substitute back

= \frac{5}{2} \cdot 1 \cdot sec (\frac{2 x}{5})

Simplify

= \frac{5}{2} sec (\frac{2 x}{5})

Add a constant to the solution

= \frac{5}{2} sec (\frac{2 x}{5}) + C

\frac{d}{d x} (ln (x) tan (x))

\frac{d}{d x} (x^{4} - 17 x^{2} + 16)

\int (ln (x) + 1) e^{x l n (x)} d x

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

x \to 3 lim (2 x^{2} + 1)

What is the integral of sec((2x)/5)tan((2x)/5) ?
The integral of sec((2x)/5)tan((2x)/5) is 5/2 sec((2x)/5)+C