What is the integral of xcos(x^2+1) ?

The integral of xcos(x^2+1) is 1/2 sin(x^2+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xcos(x^2+1)

\int x cos (x^{2} + 1) d x

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

Solution steps

\int x cos (x^{2} + 1) d x

Apply u-substitution

= \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

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

Use the common integral:

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

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

Substitute back

u = x^{2} + 1

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

Add a constant to the solution

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

What is the integral of xcos(x^2+1) ?
The integral of xcos(x^2+1) is 1/2 sin(x^2+1)+C