What is the integral of sin(7t)sec^2(cos(7t)) ?

The integral of sin(7t)sec^2(cos(7t)) is -1/7 tan(cos(7t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(7t)sec^2(cos(7t))

\int sin (7 t) sec^{2} (cos (7 t)) d t

- \frac{1}{7} tan (cos (7 t)) + C

Solution steps

\int sin (7 t) sec^{2} (cos (7 t)) d t

Apply u-substitution

: \int sin (u) sec^{2} (cos (u)) \frac{1}{7} d u

= \int sin (u) sec^{2} (cos (u)) \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int sin (u) sec^{2} (cos (u)) d u

Apply u-substitution

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

= \frac{1}{7} \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}{7} (- \int sec^{2} (v) d v)

Use the common integral:

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

= \frac{1}{7} (- tan (v))

Substitute back

= \frac{1}{7} (- tan (cos (7 t)))

Simplify

= - \frac{1}{7} tan (cos (7 t))

Add a constant to the solution

= - \frac{1}{7} tan (cos (7 t)) + C

\int \frac{x - 1}{( x - 2 ) ( x + 3 )} d x

\int e^{x} + 20 d x

\int sin (18 t) sec^{2} (cos (18 t)) d t

\int (2 x - 5) (x^{2} - 5 x + 7)^{3} d x

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

What is the integral of sin(7t)sec^2(cos(7t)) ?
The integral of sin(7t)sec^2(cos(7t)) is -1/7 tan(cos(7t))+C