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

The integral of cos(x^2)2x is sin(x^2)+C

Popular >

integral of cos(x^2)2x

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

sin (x^{2}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = x^{2}

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

Simplify

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

= sin (x^{2})

Add a constant to the solution

= sin (x^{2}) + C

n = 1 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

\int \frac{e ^{5 x}}{e ^{5 x} + 6} d x

- 2 x y - 4 x^{4} = - 2 + y

\frac{\partial}{\partial x} (12 x y - x^{3} - y^{3} - 7)

\frac{d}{d x} (\frac{18 x + 8 x ^{2}}{( 9 + 8 x ) ^{2}})