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

The integral of x/2 cos(x^2) is 1/4 sin(x^2)+C

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integral of x/2 cos(x^2)

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

\frac{1}{4} sin (x^{2}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= \frac{1}{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

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

Use the common integral:

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

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

Substitute back

u = x^{2}

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

Simplify

\frac{1}{2} \cdot \frac{1}{2} sin (x^{2}) : \frac{1}{4} sin (x^{2})

= \frac{1}{4} sin (x^{2})

Add a constant to the solution

= \frac{1}{4} sin (x^{2}) + C

y^{^{''}} + y = sin^{2} (x)

x \to - 4 - lim (∣ 5 x + 10 ∣)

\frac{- 30}{x ^{6}} + \frac{2}{x ^{2}}

\frac{d}{d x} (e^{x} + 2 e^{- x})

sin (x), cos (x), [0, 2 π]

What is the integral of x/2 cos(x^2) ?
The integral of x/2 cos(x^2) is 1/4 sin(x^2)+C