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

The integral of sec(5x)tan(5x) is 1/5 sec(5x)+C

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

\int sec (5 x) tan (5 x) d x

\frac{1}{5} sec (5 x) + C

Solution steps

\int sec (5 x) tan (5 x) d x

Apply u-substitution

: \int \frac{1}{5} d u

= \int \frac{1}{5} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{5} u

Substitute back

u = sec (5 x)

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

Add a constant to the solution

= \frac{1}{5} sec (5 x) + C

\frac{d}{d x} (sec (\frac{1}{x}))

\int \frac{1}{( x ^{2} + 9 ) ^{\frac{5}{2}}} d x

x \to 1 lim (- 1)

\int \frac{32 r ^{7} d r}{2 - r ^{8}} d x

\frac{d}{d x} (\frac{x}{2 x + 5})

What is the integral of sec(5x)tan(5x) ?
The integral of sec(5x)tan(5x) is 1/5 sec(5x)+C