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

The integral of 10*sin(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 10*sin(5x)

\int 10 \cdot 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

\int - x cos (π - x) d x

\int e^{x^{3}} \cdot 6 x^{2} d x

\int \frac{5 x ^{3}}{( x ^{4} - 8 ) ^{3}} d x

\int \frac{1}{x 49 - x ^{2}} d x

\int \frac{4}{3 x + 5} d x