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int ( x ln x )/( (x^(2) - 1)^(3//2) ) dx...

` int ( x ln x )/( (x^(2) - 1)^(3//2) ) dx `

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Verified by Experts

The correct Answer is:
` arc sec x - ( ln x)/( sqrt( x^(2) - 1)) + C `
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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -2 (SECTION -A (INDEFINITE INTEGRATION ) )
  1. int ( x^(5) +3x^(4) -x^(3) +8x^(2) -x+8)/( x^(2) + 1) dx

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  2. int ( (sqrtx+1) dx)/( sqrtx (""^(3) sqrtx+1))

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  3. int ( x ln x )/( (x^(2) - 1)^(3//2) ) dx

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  4. int ( cot x dx )/( (1- sin x) ( sec x + 1))

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  5. int ( 3x^(2) +1)/( (x^(2) - 1)^(3) )dx

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  6. निम्न अनिश्चित समाकलनों को ज्ञात कीजिए : int((ax^(2)-b)dx)/(xsqrt(c^...

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  7. int (dx)/( (x+ sqrt(x(1+x)))^(2))

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  8. int underline (( e^(sqrtx)-e^(-sqrtx))cos ( e^(sqrtx)+ e^(-sqrtx)+(pi)...

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  9. int e^(sin x) (x cos^(3)x-sin x)/(cos^(2)x)dx किसके बराबर है?

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  10. निम्न अनिश्चित समाकलनों को ज्ञात कीजिए : int(5x^(4)+4x^(5))/((x^(5)+...

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  11. निम्न अनिश्चित समाकलनों को ज्ञात कीजिए : int(sinx)^(-11//3)(cosx)^(-...

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  12. मान ज्ञात कीजिए int (dx)/(sqrt(sin ^(3) x sin (x+alpha))).

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  13. int(dx)/( sin x + secx )

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  14. int ( (1+ x^(2))dx) /( 1-2x^(2) cos alpha +x^(4))alpha in (0, pi)

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  15. int ( 4x^(5) -7x^(4) +8x^(3) -2x^(2) + 4x -7)/( x^(2)( x^(2) +1) ^(2))...

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  16. int ( f'(x) g(x) -g' (x) f(x))/( (f( x)+ g(x) ) sqrt( f(x) g(x) - g^(...

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  17. int (dx)/( cos ^(3) x - sin ^(3) x)

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  18. यदि फलन f(x)= ( sin ^(4) x)/( cos ^(2) x) का x के सापेक्ष समाकलन ta...

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  19. माना (d)/(dx) (f (x)) = ( (sin ^(12) x - cos ^(12) x))/( (sin ^(2) x...

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  20. यदि int ( ((1)/( x^(2))+( 1)/(x)) (x-1) dx)/( ((1)/( x^(3))+( 1)/(x))...

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