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int(cos8x-1)/(tan2x-cot2x)dx...

`int(cos8x-1)/(tan2x-cot2x)dx`

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`∫(cos8x+1​)/(cot2x−tan2x)dx`
`=∫(2cos^2(4x)−1+1)/((cos2x​)/(sin2x)−(sin2x)/(cos2x))​​dx`
`=∫(2cos^2(4x)sin2xcos2x​)/(cos^2(2x)−sin^2(2x))dx`
`=∫(cos^2(4x)sin4x)/(cos4x)​dx`
...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. intx^(sinx) ((sinx)/x+cosxdotlogx) dx is equal to (A) x^(sinx)+C (B...

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  2. Integration of 1/(1+((log)e x)^2) with respect to (log)e x is (tan^(-1...

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  3. int(cos8x-1)/(tan2x-cot2x)dx

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  4. If int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C , then a= -1//2 (b...

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  5. int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C ...

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  6. If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal...

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  7. int1/(1+tanx)\ dx=

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  8. int|x|^3\ dx is equal to ( x^4)/4+C (b) (|x|^4)/4+C (c) (x^4)/4+C (d) ...

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  9. Evaluate: int(cossqrt(x))/(sqrt(x))\ dx

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  10. inte^x(1-cotx+cot^2x)dx= e^xcotx+C (b) e^xcotx+C (c) e^x\ cos e c\ ...

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  11. int(sin^6x)/(cos^8x)\ dx= tan7x+C (b) (tan^7x)/7+C (c) (tan7x)/7+C (d...

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  12. int1/(7+5cosx)\ dx= 1/(sqrt(6))tan^(-1)(1/(sqrt(6))tanx/2)+C (b) 1/(s...

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  13. int1/(1+cosx+sinx)\ dx= log|1+cotx/2|+C (b) log|1-tanx/2|+C (c) log|...

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  14. int(x+3)/((x+4)^2)e^x\ dx= (e^x)/(x+4)+C (b) (e^x)/(x+3)+C (c) 1/((x+...

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  15. int(sinx)/(3+4cos^2x)\ dx log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((...

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  16. int e^x ((1-sinx)/(1-cosx)) dx= (A) e^xtan(x/2)+C (B) e^xcot(x/...

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  17. int2/((e^x+e^(-x))^2)\ dx ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x)...

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  18. int(e^x(1+x))/(cos^2(x e^x))\ dx= 2(log)ecos(x e^x)+C (b) sec(x e^x)+...

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  19. int(sin^2x)/(cos^4x)\ dx= 1/3tan^2x+C (b) 1/2tan^2x+C (c) 1/3tan^3x+C...

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  20. The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is...

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