What is the integral of 10sin(2x) ?

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

Popular >

integral of 10sin(2x)

\int 10 sin (2 x) d x

- 5 cos (2 x) + C

Solution steps

\int 10 sin (2 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 (2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= 10 \cdot \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= 10 \cdot \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= 10 \cdot \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

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

Simplify

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

= - 5 cos (2 x)

Add a constant to the solution

= - 5 cos (2 x) + C

\int \frac{x ^{2}}{( 9 - x ^{2} ) ^{\frac{5}{2}}} d x

\int \frac{d}{1} (sin (x)) d x

\int 1 e^{- θ} cos (7 θ) d θ

\int \frac{9 x ^{3} - 6 x + 2}{x ^{3} - x ^{2}} d x

\int \frac{4 x}{100 + x ^{2}} d x