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

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

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integral of 5sec(x)tan(x)

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

5 sec (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int 1 d u

= 5 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 1 \cdot u

Substitute back

u = sec (x)

= 5 \cdot 1 \cdot sec (x)

Simplify

= 5 sec (x)

Add a constant to the solution

= 5 sec (x) + C

\frac{\partial}{\partial x} (- 2 x^{2} y - y)

\int - sin (x) + cos (x) d x

\int \frac{1}{x ^{2} + 625} d x

x \to 0 lim (\frac{∣ x ∣}{x ^{3} - 5})

y = 8 x^{2} - 5 x^{11}

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