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

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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

= \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

: \int 1 d v

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

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

3 x^{2} + 4 y (y^{^{'}}) = 0

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

\int \frac{a ^{x}}{ln ( a )} d x

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