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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 (x2 + 1)
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Answer

Derivative of x2 + 1 is 2x. Thus, we use the substitution x2 + 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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