What is the integral of 3x*cos(3-x^2) ?

The integral of 3x*cos(3-x^2) is 3/2 sin(-3+x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3x*cos(3-x^2)

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

\frac{3}{2} sin (- 3 + x^{2}) + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int x cos (3 - x^{2}) d x

Factor

3 - x^{2} : - (- 3 + x^{2})

= 3 \cdot \int x cos (- (- 3 + x^{2})) d x

Simplify

x cos (- (- 3 + x^{2})) : x cos (- 3 + x^{2})

= 3 \cdot \int x cos (- 3 + x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{2} d u

= 3 \cdot \int \frac{cos ( u )}{2} d u

Take the constant out:

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

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

Use the common integral:

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

= 3 \cdot \frac{1}{2} sin (u)

Substitute back

u = - 3 + x^{2}

= 3 \cdot \frac{1}{2} sin (- 3 + x^{2})

Simplify

3 \cdot \frac{1}{2} sin (- 3 + x^{2}) : \frac{3}{2} sin (- 3 + x^{2})

= \frac{3}{2} sin (- 3 + x^{2})

Add a constant to the solution

= \frac{3}{2} sin (- 3 + x^{2}) + C

\int z^{- 4} d z

\int \frac{sec ( x )}{2 tan ^{2} ( x ) + 1} d x

\int e^{- x} 9 - e^{2 x} d x

\int (3 x - h)^{3} d x

What is the integral of 3x*cos(3-x^2) ?
The integral of 3x*cos(3-x^2) is 3/2 sin(-3+x^2)+C