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Integrals — Maths STD 12 Science — Question

Gujarat 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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