What is the integral of (10sin(5x)) ?

The integral of (10sin(5x)) is -2cos(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (10sin(5x))

\int (10 sin (5 x)) d x

- 2 cos (5 x) + C

Solution steps

\int 10 sin (5 x) d x

Take the constant out:

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

= 10 \cdot \int sin (5 x) d x

Apply u-substitution

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

= 10 \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

= 10 \cdot \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= 10 \cdot \frac{1}{5} (- cos (u))

Substitute back

u = 5 x

= 10 \cdot \frac{1}{5} (- cos (5 x))

Simplify

10 \cdot \frac{1}{5} (- cos (5 x)) : - 2 cos (5 x)

= - 2 cos (5 x)

Add a constant to the solution

= - 2 cos (5 x) + C

\frac{d}{d x} (6 \cdot 3^{x})

y = 2 - \frac{x}{2}, x = 2 y^{2}

\int (9 x + 2)^{2} d x

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

y^{^{''}} + 4 y^{^{'}} - 24 y = 0

What is the integral of (10sin(5x)) ?
The integral of (10sin(5x)) is -2cos(5x)+C