What is the integral of (sin(ln(4)x^2))/x ?

The integral of (sin(ln(4)x^2))/x is 1/2 \Si(ln(4)x^2)+C

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integral of (sin(ln(4)x^2))/x

\int \frac{sin ( ln ( 4 ) x ^{2} )}{x} d x

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

Solution steps

\int \frac{sin ( ln ( 4 ) x ^{2} )}{x} d x

Apply u-substitution

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

= \int \frac{sin ( 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{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

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

Substitute back

u = ln (4) x^{2}

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

Add a constant to the solution

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

\frac{- 4 e ^{(- 2 s)}}{( s ^{2} - 6 s + 8 )}

y^{^{'}} = t y

\frac{d}{d x} (y^{2} sin (x))

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

t \to 0 lim (\frac{2 e ^{t} - 2}{t})

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