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

The integral of (cos(x^2))/x is 1/2 \Ci(x^2)+C

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integral of (cos(x^2))/x

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

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

Solution steps

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

Apply u-substitution

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

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

Use the nonelementary integral:

\int \frac{cos ( x )}{x} d x = Ci (x)

= \frac{1}{2} Ci (u)

Substitute back

u = x^{2}

= \frac{1}{2} Ci (x^{2})

Add a constant to the solution

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

(\frac{1}{2})^{x - 1} + 3

x \to 1 lim (- lo g_{10} (x - 1))

\int \frac{x ^{3}}{a ^{2} - x ^{2}} d x

\frac{t ^{5} - 3 t ^{2}}{2 t}

\int \frac{x}{x + 5} d x

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