What is the integral of sin(22t)sec^2(cos(22t)) ?

The integral of sin(22t)sec^2(cos(22t)) is -1/22 tan(cos(22t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(22t)sec^2(cos(22t))

\int sin (22 t) sec^{2} (cos (22 t)) d t

- \frac{1}{22} tan (cos (22 t)) + C

Solution steps

\int sin (22 t) sec^{2} (cos (22 t)) d t

Apply u-substitution

: \int sin (u) sec^{2} (cos (u)) \frac{1}{22} d u

= \int sin (u) sec^{2} (cos (u)) \frac{1}{22} d u

Take the constant out:

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

= \frac{1}{22} \cdot \int sin (u) sec^{2} (cos (u)) d u

Apply u-substitution

: \int - sec^{2} (v) d v

= \frac{1}{22} \cdot \int - sec^{2} (v) d v

Take the constant out:

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

= \frac{1}{22} (- \int sec^{2} (v) d v)

Use the common integral:

\int sec^{2} (v) d v = tan (v)

= \frac{1}{22} (- tan (v))

Substitute back

= \frac{1}{22} (- tan (cos (22 t)))

Simplify

= - \frac{1}{22} tan (cos (22 t))

Add a constant to the solution

= - \frac{1}{22} tan (cos (22 t)) + C

\int 8 sin (2 x) - 3 cos (\frac{1}{5} x) d x

\int \frac{x}{( x + 2 ) ^{4}} d x

\int \frac{5 x - 13}{( x - 3 ) ( x - 2 )} d x

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

What is the integral of sin(22t)sec^2(cos(22t)) ?
The integral of sin(22t)sec^2(cos(22t)) is -1/22 tan(cos(22t))+C