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

The integral of x^5cos(y^4) is 1/6 x^6cos(y^4)+C

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integral of x^5cos(y^4)

\int x^{5} cos (y^{4}) d x

\frac{1}{6} x^{6} cos (y^{4}) + C

Solution steps

\int x^{5} cos (y^{4}) d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{6}}{6}

= cos (y^{4}) \frac{x ^{6}}{6}

Simplify

cos (y^{4}) \frac{x ^{6}}{6} : \frac{1}{6} x^{6} cos (y^{4})

= \frac{1}{6} x^{6} cos (y^{4})

Add a constant to the solution

= \frac{1}{6} x^{6} cos (y^{4}) + C

\frac{\partial}{\partial u} (v cos (u))

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

\frac{d}{d x} (\frac{4}{x ^{4}} - 5 3 x)

\int \frac{5}{x ^{2} + 4} d x

\int \frac{2 x ^{3} - 2 x ^{2} + 1}{x ^{2} - x} d x

What is the integral of x^5cos(y^4) ?
The integral of x^5cos(y^4) is 1/6 x^6cos(y^4)+C