Question

If $\smallint \frac{1}{{(\sin \,\,x\,\, + \,\,4)\,(\sin \,\,x - 1)}}\,\,dx$ $ = A\frac{1}{{	an \,\,\frac{x}{2} - 1}} + B{	an ^{ - 1}}\left( {f\left( x ight)} ight) + C$, then

Accepted Answer

$A = \frac{2}{5},\;\,B = \frac{{ - \,2}}{{5\,\sqrt {15} }},\;\,f\left( x ight) = \frac{{4	an \,\,x/2 + 1}}{{\sqrt {15} }}$

Answer

$A = \frac{1}{5},\,\;B = \frac{{ - \,2}}{{5\,\sqrt {15} }},\;\,f\left( x ight) = \frac{{4\,\,	an \,\,x + 3}}{{\sqrt {15} }}$

Answer

$A = - \frac{1}{5},\,\;\,B = \frac{1}{{\sqrt {15} }},\;\,f\left( x ight) = \frac{{4\,\,	an \,\,\left( {\frac{x}{2}} ight) + 1}}{{\sqrt {15} }}$

Answer

$A = \frac{2}{5},\;\,B = \frac{{ - \,2}}{5},\;\,f\left( x ight) = \frac{{4\,\,	an \,\,x + 1}}{5}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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