What is the integral of x^{31}sin(x^{32}) ?

The integral of x^{31}sin(x^{32}) is -1/32 cos(x^{32})+C

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integral of x^{31}sin(x^{32})

\int x^{31} sin (x^{32}) d x

- \frac{1}{32} cos (x^{32}) + C

Solution steps

\int x^{31} sin (x^{32}) d x

Apply u-substitution

: \int \frac{sin ( u )}{32} d u

= \int \frac{sin ( u )}{32} d u

Take the constant out:

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

= \frac{1}{32} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{32} (- cos (u))

Substitute back

u = x^{32}

= \frac{1}{32} (- cos (x^{32}))

Simplify

= - \frac{1}{32} cos (x^{32})

Add a constant to the solution

= - \frac{1}{32} cos (x^{32}) + C

x y^{^{'}} + y = 46 x

e^{(- 3 x)}

y = \frac{3 x ^{4} + 9}{x ^{2}}

\frac{x ^{3} - 2 x ^{2} + 4}{x ^{2}}

\int (ln (x + 1))^{2} d x

What is the integral of x^{31}sin(x^{32}) ?
The integral of x^{31}sin(x^{32}) is -1/32 cos(x^{32})+C