What is the integral of x^{25}sin(x^{26}) ?

The integral of x^{25}sin(x^{26}) is -1/26 cos(x^{26})+C

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integral of x^{25}sin(x^{26})

\int x^{25} sin (x^{26}) d x

- \frac{1}{26} cos (x^{26}) + C

Solution steps

\int x^{25} sin (x^{26}) d x

Apply u-substitution

: \int \frac{sin ( u )}{26} d u

= \int \frac{sin ( u )}{26} d u

Take the constant out:

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

= \frac{1}{26} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{26} (- cos (u))

Substitute back

u = x^{26}

= \frac{1}{26} (- cos (x^{26}))

Simplify

= - \frac{1}{26} cos (x^{26})

Add a constant to the solution

= - \frac{1}{26} cos (x^{26}) + C

e^{5}

\frac{\partial}{\partial x} (y^{2} sin (\frac{x}{y}))

\frac{d}{d x} (\frac{i}{5 x ^{2} + 1})

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

\int ln (4 - x) d x

What is the integral of x^{25}sin(x^{26}) ?
The integral of x^{25}sin(x^{26}) is -1/26 cos(x^{26})+C