Published by:
CGP EDU Academic Team
Published on: August 11, 2026
We are now here to learn, how to evaluate
(I) Evaluation of integrals of the form 
Algorithm :
A
Write the numerator px + q in the following form px + q = λ 
(ax2 + bx + c) + µ (II) Obtain the values of λ and µ by equating the coefficients of like powers of x on both sides. (III) Replace px + q by λ (2ax + b) + µ in the given integral to get 
dx 
On the basis of above passage, answer the following questions: (i) 
= 2 log |sin2 φ – 4 sin φ + 5| + 7 tan–1 (sin φ – 2) + c log |(sin–1x)2 + 4sin–1 x + 5)| + 2tan–1 (sin–1 x + 2) + c 1, 2
(ax2 + bx + c) + µ (II) Obtain the values of λ and µ by equating the coefficients of like powers of x on both sides. (III) Replace px + q by λ (2ax + b) + µ in the given integral to get dx On the basis of above passage, answer the following questions: (i) = 2 log |sin2 φ – 4 sin φ + 5| + 7 tan–1 (sin φ – 2) + c log |(sin–1x)2 + 4sin–1 x + 5)| + 2tan–1 (sin–1 x + 2) + c 1, 2
B
3 log |sin2 φ – 4 sin φ + 5| + 7tan–1 (sin φ – 2) + c log |(sin–1 x)2 + 4sin–1 x + 5|+ tan–1 (sin–1 x + 2) + c –1, –4
C
2 log |sin2 φ – 4 sin φ + 5| + 5 tan–1 (sin φ – 2) + c log |(sin–1 x)2 +4sin–1 x + 5|– tan–1 (sin–1x + 2) + c 1, – 4
D
None of these (ii) 
= None of these (iii) If 
= A log |( λ nx)2 + 6 λ nx + 10| + B tan–1 ( λ nx + 3) + c. then A and B respectively- None of these
= None of these (iii) If = A log |( λ nx)2 + 6 λ nx + 10| + B tan–1 ( λ nx + 3) + c. then A and B respectively- None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Ans.
(i)
Sol. 2 log |sin2 φ – 4 sin φ + 5| + 7 tan–1 (sin φ – 2) + c
(ii)
Sol. log |(sin–1 x)2 + 4sin–1 x + 5| + tan–1 (sin–1 x + 2) + c
(iii)
Sol. 1, – 4
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