99 Percentile Qs Bank for JEE MainMathematicsIndefinite Integration

If a x-2 x b x+5 x d x= 7 41 x+ 22 7 |b x+5 x|+C,(a>0, b>0) , then d x b+a x =

Options

A2 3 ( 3 x 2 +4- 3 3 x 2 +4+ 3 )+C
B2 7 ⁻¹ ( x 2 7 )+C
C2 7 ( 7 - x 2 7 + x 2 )+C
D2 ⁻¹ ( 2 x 2 1+ ^2 x 2 )+C

Correct answer

B. 2 7 ⁻¹ ( x 2 7 )+C

Step-by-step solution

We have, a x-2 x b x+5 x d x= 7 41 x+ 22 41 aligned & |(b x+5 x)|+C & Now, let a x-2 x= (b x+5 x) & + (b x-5 x) aligned a=5 + b and -2=b -5 But it is given, = 7 41 and = 22 41 a=3, b=4 d x b+a x = d x 4+3 x = (1+ ^2 x 2 ) d x 4 (1+ ^2 x 2 )+3 (1- ^2 x 2 ) aligned &= ^2 x / 2 7+ ^2 x / 2 d x & x 2 =t ^2 x 2 d x=2 d t & d x b+a x =2 d t 7+t^2 &= 2 7 ⁻¹ t 7 +C &= 2 7 ⁻¹ ( x / 2 7 )+C aligned

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