What is the integral of cos(4x^2) ?

The integral of cos(4x^2) is (sqrt(pi))/(2sqrt(2))\C(2sqrt(2/pi)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(4x^2)

\int cos (4 x^{2}) d x

\frac{π}{2 2} C (2 \frac{2}{π} x) + C

Solution steps

\int cos (4 x^{2}) d x

Apply Integral Substitution

= \int \frac{1}{2} 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^{2}) d u

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= \frac{1}{2} \frac{π}{2} C (\frac{2}{π} u)

Substitute back

u = 2 x

= \frac{1}{2} \frac{π}{2} C (\frac{2}{π} \cdot 2 x)

Simplify

\frac{1}{2} \frac{π}{2} C (\frac{2}{π} \cdot 2 x) : \frac{π}{2 2} C (2 \frac{2}{π} x)

= \frac{π}{2 2} C (2 \frac{2}{π} x)

Add a constant to the solution

= \frac{π}{2 2} C (2 \frac{2}{π} x) + C

\int (x + x ln (x))^{- 1} d x

\int cos (a \cdot x) d x

\int \frac{x ^{2}}{x ^{4} - 3 x ^{2} + 2} d x

\int y^{2} e^{x} d x

\int 3 1 + 3 sin (x) cos (x) d x

What is the integral of cos(4x^2) ?
The integral of cos(4x^2) is (sqrt(pi))/(2sqrt(2))\C(2sqrt(2/pi)x)+C