What is the integral of 20sec(4x)tan(4x) ?

The integral of 20sec(4x)tan(4x) is 5sec(4x)+C

Popular >

integral of 20sec(4x)tan(4x)

\int 20 sec (4 x) tan (4 x) d x

5 sec (4 x) + C

Solution steps

\int 20 sec (4 x) tan (4 x) d x

Take the constant out:

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

= 20 \cdot \int sec (4 x) tan (4 x) d x

Apply u-substitution

: \int \frac{1}{4} d u

= 20 \cdot \int \frac{1}{4} d u

Integral of a constant:

\int a d x = a x

= 20 \cdot \frac{1}{4} u

Substitute back

u = sec (4 x)

= 20 \cdot \frac{1}{4} sec (4 x)

Simplify

20 \cdot \frac{1}{4} sec (4 x) : 5 sec (4 x)

= 5 sec (4 x)

Add a constant to the solution

= 5 sec (4 x) + C

\int \frac{3 x ^{2}}{25 - x ^{2}} d x

x \to 7 lim (cos (\frac{π x}{3}))

y = 3 x

x \to 3 lim (2 x^{3} + 4 x - 2)

\frac{d}{d x} (2 a x)

What is the integral of 20sec(4x)tan(4x) ?
The integral of 20sec(4x)tan(4x) is 5sec(4x)+C