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

The integral of 2pixsin(x^2) is -picos(x^2)+C

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integral of 2pixsin(x^2)

\int 2 π x sin (x^{2}) d x

- π cos (x^{2}) + C

Solution steps

\int 2 π x sin (x^{2}) d x

Take the constant out:

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

= 2 π \cdot \int x sin (x^{2}) d x

Apply u-substitution

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

= 2 π \cdot \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

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

Use the common integral:

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

= 2 π \frac{1}{2} (- cos (u))

Substitute back

u = x^{2}

= 2 π \frac{1}{2} (- cos (x^{2}))

Simplify

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

= - π cos (x^{2})

Add a constant to the solution

= - π cos (x^{2}) + C

\frac{d y}{d x}, x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

\int t^{2} + 1 d t

\frac{d}{d x} (x - 2 y)

f (x) = x^{2} - 2 x - 8, at x = - 2

What is the integral of 2pixsin(x^2) ?
The integral of 2pixsin(x^2) is -picos(x^2)+C