What is the integral of-5sin(5x) ?

The integral of-5sin(5x) is cos(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-5sin(5x)

\int - 5 sin (5 x) d x

cos (5 x) + C

Solution steps

\int - 5 sin (5 x) d x

Take the constant out:

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

= - 5 \cdot \int sin (5 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{5} d u

= - 5 \cdot \int sin (u) \frac{1}{5} d u

Take the constant out:

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

= - 5 \cdot \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - 5 \cdot \frac{1}{5} (- cos (u))

Substitute back

u = 5 x

= - 5 \cdot \frac{1}{5} (- cos (5 x))

Simplify

- 5 \cdot \frac{1}{5} (- cos (5 x)) : cos (5 x)

= cos (5 x)

Add a constant to the solution

= cos (5 x) + C

f (y) = 4 y^{2}

\frac{d}{d x} (x lo g_{2} (x - 3))

(ln (t))^{^{'}}

\frac{3 x - 5}{x ^{2} - 1}

x \to - 2 lim ((x^{3}) (5 - 3 x^{2}))