What is the integral of (2xsin(x^2)) ?

The integral of (2xsin(x^2)) is -cos(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 (2xsin(x^2))

\int (2 x sin (x^{2})) d x

- cos (x^{2}) + C

Solution steps

\int 2 x sin (x^{2}) d x

Take the constant out:

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

= 2 \cdot \int x sin (x^{2}) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = x^{2}

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

Simplify

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

= - cos (x^{2})

Add a constant to the solution

= - cos (x^{2}) + C

\int sin (x) x d x

x y^{2} y^{^{'}} = 2 - y^{3}

y = x - 3, y^{2} = 2 x + 18

f (x) = \frac{1}{2 + 3 x}, at x = 2

\int \frac{13}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

What is the integral of (2xsin(x^2)) ?
The integral of (2xsin(x^2)) is -cos(x^2)+C