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`int1/(cosx+sqrt(3)sinx)\ dx` is equal to (a) `logtan(pi/3+x/2)+C` (b) `logtan(x/2-pi/3)+C` (c) `1/2logtan(x/2+pi/3)+C` (d) none of these

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RD SHARMA ENGLISH-INDEFINITE INTEGRALS-All Questions
  1. Evaluate: int1/(sin^2xcos^2x)\ dx

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  2. intx/(4+x^4)\ dx is equal to 1/4tan^(-1)x^2 (b) 1/4tan^(-1)((x^2)/2) (...

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  3. int1/(cosx+sqrt(3)sinx)\ dx is equal to (a) logtan(pi/3+x/2)+C (b) log...

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  4. intxsecx^2\ dx is equal to 1/2log(secx^2+tanx^2)+C (b) (x^2)/2log(secx...

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  5. If int1/(5+4sinx)\ dx=Atan^(-1)(Btanx/2+4/3)+C , then A=2/3,\ \ B=5/3 ...

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

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

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

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

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

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

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

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

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

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

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

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

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