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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Integrate the function w.r.t. x: $2x \sin (x^2 + 1)$
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Answer

Derivative of $x^2 + 1$ is $2x.$
Thus, we use the substitution $x^2 + 1 = t$
so that $2x\ dx = dt.$
Therefore, $\int 2 x \sin \left(x^{2}+1\right) d x=\int \sin t d t=-\cos t+C=-\cos \left(x^{2}+1\right)+C$ 

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