What is the integral of x^5cos(x^6) ?

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

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integral of x^5cos(x^6)

\int x^{5} cos (x^{6}) d x

\frac{1}{6} sin (x^{6}) + C

Solution steps

\int x^{5} cos (x^{6}) d x

Apply u-substitution

: \int \frac{cos ( u )}{6} d u

= \int \frac{cos ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{6} sin (u)

Substitute back

u = x^{6}

= \frac{1}{6} sin (x^{6})

Add a constant to the solution

= \frac{1}{6} sin (x^{6}) + C

\frac{d}{d x} (- x + \frac{2}{x} + 1)

\int_{0}^{1} - 5 x 5^{x} d x

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

\frac{d}{d x} (\frac{3 x}{1 - x})

\int \frac{( x ^{\frac{1}{3}} )}{x ^{\frac{2}{3}}} d x

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