What is the integral of 5sin(x^4) ?

The integral of 5sin(x^4) is i 5/8 x(\E_{3/4}(-ix^4)-\E_{3/4}(ix^4))+C

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integral of 5sin(x^4)

\int 5 sin (x^{4}) d x

i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) + C

Solution steps

\int 5 sin (x^{4}) d x

Take the constant out:

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

= 5 \cdot \int sin (x^{4}) d x

Use the nonelementary integral:

\int sin (x^{4}) d x = \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

= 5 \cdot \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

Simplify

5 \cdot \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) : i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

= i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

Add a constant to the solution

= i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) + C

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What is the integral of 5sin(x^4) ?
The integral of 5sin(x^4) is i 5/8 x(\E_{3/4}(-ix^4)-\E_{3/4}(ix^4))+C