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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Find $\int \cos 6 x \sqrt{1+\sin 6 x} d x$
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Answer

Put t = 1 + sin 6x, so that dt = 6 cos 6x dx
Therefore $\int \cos 6 x \sqrt{1+\sin 6 x} d x$ = $\frac{1}{6} \int t^{\frac{1}{2}} d t$
= $\frac{1}{6} \times \frac{2}{3}(t)^{\frac{3}{2}}+\mathrm{C}=\frac{1}{9}(1+\sin 6 x)^{\frac{3}{2}}+\mathrm{C}$

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