What is the integral of x^{11}sin(x^{12}) ?

The integral of x^{11}sin(x^{12}) is -1/12 cos(x^{12})+C

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integral of x^{11}sin(x^{12})

\int x^{11} sin (x^{12}) d x

- \frac{1}{12} cos (x^{12}) + C

Solution steps

\int x^{11} sin (x^{12}) d x

Apply u-substitution

: \int \frac{sin ( u )}{12} d u

= \int \frac{sin ( u )}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{12} (- cos (u))

Substitute back

u = x^{12}

= \frac{1}{12} (- cos (x^{12}))

Simplify

= - \frac{1}{12} cos (x^{12})

Add a constant to the solution

= - \frac{1}{12} cos (x^{12}) + C

x + 4 ln (x + 10) - ln (2 x + 1)

\frac{2}{( 3 s + 1 )}

\int_{- 2}^{2} \frac{e ^{x}}{e ^{x} - 1} d x

\frac{d}{d x} (x e^{x s i n (x)})

\int \frac{sin ( u )}{u} d u

What is the integral of x^{11}sin(x^{12}) ?
The integral of x^{11}sin(x^{12}) is -1/12 cos(x^{12})+C