What is the integral of ycos(x^5) ?

The integral of ycos(x^5) is y(\Gamma(1/5 ,-ix^5)-\Gamma(1/5 ,ix^5))/(10\sqrt[10]{-1)}+C

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integral of ycos(x^5)

\int y cos (x^{5}) d x

y \frac{Γ ( \frac{1}{5} , - i x ^{5} ) - Γ ( \frac{1}{5} , i x ^{5} )}{10 10 - 1} + C

Solution steps

\int y cos (x^{5}) d x

Take the constant out:

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

= y \cdot \int cos (x^{5}) d x

Use the nonelementary integral:

\int cos (x^{5}) d x = \frac{Γ ( \frac{1}{5} , - i x ^{5} ) - Γ ( \frac{1}{5} , i x ^{5} )}{10 10 - 1}

= y \frac{Γ ( \frac{1}{5} , - i x ^{5} ) - Γ ( \frac{1}{5} , i x ^{5} )}{10 10 - 1}

Add a constant to the solution

= y \frac{Γ ( \frac{1}{5} , - i x ^{5} ) - Γ ( \frac{1}{5} , i x ^{5} )}{10 10 - 1} + C

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What is the integral of ycos(x^5) ?
The integral of ycos(x^5) is y(\Gamma(1/5 ,-ix^5)-\Gamma(1/5 ,ix^5))/(10\sqrt[10]{-1)}+C