What is the integral of 2^3sin(x^2) ?

The integral of 2^3sin(x^2) is 4sqrt(2)sqrt(pi)\S(sqrt(2/pi)x)+C

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integral of 2^3sin(x^2)

\int 2^{3} sin (x^{2}) d x

42 π § (\frac{2}{π} x) + C

Solution steps

\int 2^{3} sin (x^{2}) d x

Take the constant out:

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

= 2^{3} \cdot \int sin (x^{2}) d x

Simplify

= 8 \cdot \int sin (x^{2}) d x

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= 8 \frac{π}{2} § (\frac{2}{π} x)

Simplify

8 \frac{π}{2} § (\frac{2}{π} x) : 42 π § (\frac{2}{π} x)

= 42 π § (\frac{2}{π} x)

Add a constant to the solution

= 42 π § (\frac{2}{π} x) + C

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

\frac{d x}{d t} = \frac{x ^{3} - x t ^{2}}{t ^{3}}, x (1) = 2

\int 3 x^{2} + 2 x + 4 d x

\frac{d}{d x} (2.1 + e^{2} - \frac{π ^{2}}{20})

\frac{d}{d x} (x^{3} + 4 x^{2})

What is the integral of 2^3sin(x^2) ?
The integral of 2^3sin(x^2) is 4sqrt(2)sqrt(pi)\S(sqrt(2/pi)x)+C