What is the integral of cos(t^4) ?

The integral of cos(t^4) is -1/8 t(\E_{3/4}(-it^4)+\E_{3/4}(it^4))+C

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integral of cos(t^4)

\int cos (t^{4}) d t

- \frac{1}{8} t (E_{\frac{3}{4}} (- i t^{4}) + E_{\frac{3}{4}} (i t^{4})) + C

Solution steps

\int cos (t^{4}) d t

Use the nonelementary integral:

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

= - \frac{1}{8} t (E_{\frac{3}{4}} (- i t^{4}) + E_{\frac{3}{4}} (i t^{4}))

Add a constant to the solution

= - \frac{1}{8} t (E_{\frac{3}{4}} (- i t^{4}) + E_{\frac{3}{4}} (i t^{4})) + C

What is the integral of cos(t^4) ?
The integral of cos(t^4) is -1/8 t(\E_{3/4}(-it^4)+\E_{3/4}(it^4))+C