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Q.

If I=∫5−x2+xdx,  then I  equals

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a

x+25−x+3sin−1x+23+C

b

x+25−x+7sin−1x+27+C

c

x+25−x+5sin−1x+25+C

d

x+25−x+5sin−1x+2+C

answer is B.

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Detailed Solution

Put 2+x=t2,  so that dx=2t  dt,  thenI=∫7−t2t(2t)dt    =2∫7−t2dt =t7−t2+7sin−1(t7)+C=x+25−x+7sin−1(x+27)+C
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