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Integration of 1/(1+((log)e x)^2) with r...

Integration of `1/(1+((log)_e x)^2)` with respect to `(log)_e x` is `(tan^(-1)((log)_e x)/x)+C` (b) `tan^(-1)((log)_e x)+C` (c) `(tan^(-1)x)/x+C` (d) none of these

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RD SHARMA ENGLISH-INDEFINITE INTEGRALS-All Questions
  1. If int1/(5+4sinx)\ dx=Atan^(-1)(Btanx/2+4/3)+C , then A=2/3,\ \ B=5/3 ...

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  2. intx^(sinx) ((sinx)/x+cosxdotlogx) dx is equal to (A) x^(sinx)+C (B...

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

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

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

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

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

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  9. int|x|^3\ dx is equal to (a) (- x^4)/4+C (b) (|x|^4)/4+C (c) (x^4)/4+C...

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

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

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

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

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

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

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

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

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

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

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  20. Evaluateint(sin^2x)/(cos^4x)\ dx= (a)1/3tan^2x+C (b) 1/2tan^2x+C (...

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