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(A) To integrate $\int 2 x \sin \left(x^{2}+1\right) d x$,we use the method of substitution.Let $t = x^{2}+1$.Then,differentiating both sides with res

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$-\cos \left(x^{2}+1\right)+C$

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(A) To integrate $\int 2 x \sin \left(x^{2}+1\right) d x$,we use the method of substitution.Let $t = x^{2}+1$.Then,differentiating both sides with respect to $x$,we get $\frac{dt}{dx} = 2x$,which implies $dt = 2x \, dx$.Substituting these into the integral,we get:$\int \sin(t) \, dt = -\cos(t) + C$.Finally,substituting $t = x^{2}+1$ back into the expression,we obtain:$-\cos \left(x^{2}+1\right) + C$.

Integrate the following function with respect to $x:$
$2 x \sin \left(x^{2}+1\right)$

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Integrate the following function with respect to $x:$$2 x \sin \left(x^{2}+1\right)$