Question

1. $\int 2x\cos (x^{2}-3)dx$

Explanation:

Step1: Substitute

Let \( u = x^{2}-3 \), then \( du=2x dx \).

Step2: Integrate

The integral \( \int 2x\cos(x^{2} - 3)dx=\int\cos(u)du \).
Since \( \int\cos(u)du=\sin(u)+C \).

Step3: Back - substitute

Substitute \( u = x^{2}-3 \) back, we get \( \sin(x^{2}-3)+C \).

Answer:

\(\sin(x^{2}-3)+C\)