What is the integral from 1 to 2 of (cos(x^2))/x ?

The integral from 1 to 2 of (cos(x^2))/x is 1/2 (\Ci(4)-\Ci(1))

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integral from 1 to 2 of (cos(x^2))/x

\int_{1}^{2} \frac{cos ( x ^{2} )}{x} d x

\frac{1}{2} (Ci (4) - Ci (1))

Decimal

- 0.2391928104

Solution steps

\int_{1}^{2} \frac{cos ( x ^{2} )}{x} d x

Apply u-substitution

= \int_{1}^{4} \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_{1}^{4} \frac{cos ( u )}{u} d u

Use the nonelementary integral:

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

= \frac{1}{2} [Ci (u)]_{1}^{4}

Compute the boundaries:

Ci (4) - Ci (1)

= \frac{1}{2} (Ci (4) - Ci (1))

What is the integral from 1 to 2 of (cos(x^2))/x ?
The integral from 1 to 2 of (cos(x^2))/x is 1/2 (\Ci(4)-\Ci(1))