Integrate the function w.r.t. $x$: $2x \sin (x^2 + 1)$
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $-\cos (x^2 + 1) + C$
Derivative of $x^2 + 1$ is $2x$. Thus, we use the substitution $x^2 + 1 = t$ so that $2x \, dx = dt$.
Therefore, $\int 2x \sin (x^2 + 1) \, dx = \int \sin t \, dt = -\cos t + C = -\cos (x^2 + 1) + C$