What is the integral of x^2(x^3+5)^8cos((x^3+5)^9) ?

The integral of x^2(x^3+5)^8cos((x^3+5)^9) is 1/27 sin((x^3+5)^9)+C

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integral of x^2(x^3+5)^8cos((x^3+5)^9)

\int x^{2} (x^{3} + 5)^{8} cos ((x^{3} + 5)^{9}) d x

\frac{1}{27} sin ((x^{3} + 5)^{9}) + C

Solution steps

\int x^{2} (x^{3} + 5)^{8} cos ((x^{3} + 5)^{9}) d x

Apply u-substitution

: \int \frac{cos ( u )}{27} d u

= \int \frac{cos ( u )}{27} d u

Take the constant out:

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

= \frac{1}{27} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{27} sin (u)

Substitute back

u = (x^{3} + 5)^{9}

= \frac{1}{27} sin ((x^{3} + 5)^{9})

Add a constant to the solution

= \frac{1}{27} sin ((x^{3} + 5)^{9}) + C

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

x y^{^{'}} + 2 y = - 4 x

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

\int \frac{1}{u 2 - u ^{2}} d u

n = 1 \sum \infty \frac{1}{2}

What is the integral of x^2(x^3+5)^8cos((x^3+5)^9) ?
The integral of x^2(x^3+5)^8cos((x^3+5)^9) is 1/27 sin((x^3+5)^9)+C