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Step-by-step Solution

Solve the trigonometric integral $\int24x^2\cos\left(8x^3\right)dx$

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Answer

$\sin\left(8x^3\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }\left(24x^2cos\left(8x^3\right)\right)dx$
1

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

$24\int x^2\cos\left(8x^3\right)dx$
2

Solve the integral $\int x^2\cos\left(8x^3\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^3 \\ du=3x^{2}dx\end{matrix}$

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Answer

$\sin\left(8x^3\right)+C_0$
$\int_{ }^{ }\left(24x^2cos\left(8x^3\right)\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

4. See formulas

Time to solve it:

~ 0.79 seconds