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

The integral of sec(4x+4)tan(4x+4) is 1/4 sec(4x+4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{4} sec (4 x + 4) + C

Solution steps

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

Apply u-substitution

: \int sec (u) tan (u) \frac{1}{4} d u

= \int sec (u) tan (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sec (u) tan (u) d u

Apply u-substitution

: \int 1 d v

= \frac{1}{4} \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{4} \cdot 1 \cdot v

Substitute back

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

Simplify

= \frac{1}{4} sec (4 x + 4)

Add a constant to the solution

= \frac{1}{4} sec (4 x + 4) + C

\int \frac{e ^{2 s}}{e ^{2 s} + 1} d s

\int 6 x e^{2 x} d x

\int cos^{3} (x) sin^{10} (x) d x

\int (16 - x^{2}) d x

What is the integral of sec(4x+4)tan(4x+4) ?
The integral of sec(4x+4)tan(4x+4) is 1/4 sec(4x+4)+C