What is the integral of 10cos(sqrt(3x)) ?

The integral of 10cos(sqrt(3x)) is 20/3 (sqrt(3)sqrt(x)sin(sqrt(3)sqrt(x))+cos(sqrt(3)sqrt(x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 10cos(sqrt(3x))

\int 10 cos (3 x) d x

\frac{20}{3} (3 x sin (3 x) + cos (3 x)) + C

Solution steps

\int 10 cos (3 x) d x

Take the constant out:

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

= 10 \cdot \int cos (3 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{3} d u

= 10 \cdot \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= 10 \cdot \frac{1}{3} \cdot \int cos (u) d u

Apply u-substitution

: \int cos (v) \cdot 2 v d v

= 10 \cdot \frac{1}{3} \cdot \int cos (v) \cdot 2 v d v

Take the constant out:

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

= 10 \cdot \frac{1}{3} \cdot 2 \cdot \int cos (v) v d v

Apply Integration By Parts

: v sin (v) - \int sin (v) d v

= 10 \cdot \frac{1}{3} \cdot 2 (v sin (v) - \int sin (v) d v)

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

= 10 \cdot \frac{1}{3} \cdot 2 (v sin (v) - (- cos (v)))

Substitute back

= 10 \cdot \frac{1}{3} \cdot 2 (3 x sin (3 x) - (- cos (3 x)))

Simplify

10 \cdot \frac{1}{3} \cdot 2 (3 x sin (3 x) - (- cos (3 x))) : \frac{20}{3} (3 x sin (3 x) + cos (3 x))

= \frac{20}{3} (3 x sin (3 x) + cos (3 x))

Add a constant to the solution

= \frac{20}{3} (3 x sin (3 x) + cos (3 x)) + C

\frac{d}{d x} (\frac{x ^{2}}{4} \cdot sin (x - 2))

\int x^{4} (x^{2} - 3 x)^{2} d x

y^{^{''}} + 4 y = tan (2 t)

\int \frac{- sin ( x )}{cos ( x )} d x

\int \frac{2 x}{x ^{2} - 4} d x

What is the integral of 10cos(sqrt(3x)) ?
The integral of 10cos(sqrt(3x)) is 20/3 (sqrt(3)sqrt(x)sin(sqrt(3)sqrt(x))+cos(sqrt(3)sqrt(x)))+C