Evaluate the indefinite integral.
(Use symbolic notation and fractions where needed. Use $C$ for the arbitrary constant. Absorb into $C$ as much as possible.)
\[
\int 8 \theta \sin \left(8 \theta^{2}\right) d \theta=
\]

Answer

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Answer

The indefinite integral of $8 \theta \sin \left(8 \theta^{2}\right)$ is $\boxed{-\frac{1}{2}\cos \left(8 \theta^{2}\right) + C}$.

Steps

Step 1 ：Define the function to be integrated as $f = 8 \theta \sin \left(8 \theta^{2}\right)$.

Step 2 ：Perform the integration to find the integral of the function, which is $-\cos \left(8 \theta^{2}\right) / 2$.

Step 3 ：Simplify the result of the integration to get $-\cos \left(8 \theta^{2}\right) / 2$.

Step 4 ：Add the constant of integration $C$ to the result.

Step 5 ：The indefinite integral of $8 \theta \sin \left(8 \theta^{2}\right)$ is $\boxed{-\frac{1}{2}\cos \left(8 \theta^{2}\right) + C}$.