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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫ esin⁡θ [log⁡  sin⁡  θ+  cosec2 θ]  cos⁡  θ dθ\int \,{e^{\sin \mathrm{\theta }}}\,[\log \,\,\sin \,\,\mathrm{\theta } + \,\,\mathrm{cose}{\mathrm{c}^2}\,\mathrm{\theta }]\,\,\cos \,\,\mathrm{\theta }\,d\mathrm{\theta } is equal to
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Correct option: C
esin⁡θ  [log⁡  sin⁡  θ  −  cosec  θ]  +  c{e^{\sin \mathrm{\theta }}}\,\,\left[ {\log \,\,\sin \,\,\mathrm{\theta }\,\, - \,\,\mathrm{cosec}\,\,\mathrm{\theta }} \right]\,\, + \,\,c
The correct answer is e(sin θ) [log sin θ - cosec θ] + c because integrating by parts and simplifying leads to this result.

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