Problem

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

Solution

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 \(\boxed{-\frac{1}{2}\cos \left(8 \theta^{2}\right) + C}\).

From Solvely APP
Source: https://solvelyapp.com/problems/th9KUNCfl9/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download