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

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

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

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

Solution steps

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

Factor

x^{2} - 1 : - (- x^{2} + 1)

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

Simplify

x cos (- (- x^{2} + 1)) : x cos (1 - x^{2})

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

Apply u-substitution

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

= \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 = 1 - x^{2}

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

Add a constant to the solution

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

\int (1 + 4 x^{2}) d x

\int (7) d x

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

\int \frac{x - 1}{x ^{2} + 5 x + 6} d x

\int tan^{- 8} (x) sec^{4} (x) d x

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