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

The integral of xsin(x^2) is -1/2 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 xsin(x^2)

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

- \frac{1}{2} cos (x^{2}) + C

Solution steps

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

Apply u-substitution

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

= \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

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

Use the common integral:

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

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

Substitute back

u = x^{2}

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

Simplify

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

Add a constant to the solution

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

\int x^{2} e^{- x^{3}} d x

\int 10 sec (2 x) tan (2 x) d x

\int cosh (x) sinh (x) d x

\int \frac{7}{2 x} d x

y^{^{'}} = \frac{( x ^{2} y ^{4} + 3 x ^{2} )}{y ^{3}}

What is the integral of xsin(x^2) ?
The integral of xsin(x^2) is -1/2 cos(x^2)+C