What is the integral from x^2 to x of (sin(xt))/t ?

The integral from x^2 to x of (sin(xt))/t is \Si(x^2)-\Si(x^3)

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integral from x^2 to x of (sin(xt))/t

\int_{x^{2}}^{x} \frac{sin ( x t )}{t} d t

Si (x^{2}) - Si (x^{3})

Solution steps

\int_{x^{2}}^{x} \frac{sin ( x t )}{t} d t

Apply u-substitution

= \int_{x^{3}}^{x^{2}} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= [Si (u)]_{x^{3}}^{x^{2}}

Compute the boundaries:

Si (x^{2}) - Si (x^{3})

= Si (x^{2}) - Si (x^{3})

What is the integral from x^2 to x of (sin(xt))/t ?
The integral from x^2 to x of (sin(xt))/t is \Si(x^2)-\Si(x^3)