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intfrac{1}{4+5sin x}dx=..............a)(...

`intfrac{1}{4+5sin x}dx=`..............a)`(1/3)log |frac{2tan(x/2)+4}{2tan(x/2)+1}|+c` b)`(1/6)log |frac{2tan(x/2)+4}{2tan(x/2)+1}|+c` c)`(1/3)log |frac{2tan(x/2)+1}{2tan(x/2)+4}|+c` d)`(1/6)log |frac{2tan(x/2)+1}{2tan(x/2)+4}|+c`

A

(1/3) log |`frac { 2 tan (x/2) + 4}{2 tan (x/2) + 1}`| + c

B

(1/6) log |`frac { 2 tan (x/2) + 4}{2 tan (x/2) + 1}`| + c

C

(1/3) log |`frac { 2 tan (x/2) + 1}{2 tan (x/2) + 4}`| + c

D

(1/6) log |`frac { 2 tan (x/2) +1}{2 tan (x/2) + 4}`| + c

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CHETANA PUBLICATION-Indefinite Integration-Exercise
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  3. intfrac{1}{4+5sin x}dx=..............a)(1/3)log |frac{2tan(x/2)+4}{2ta...

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  4. int sqrt (frac{a+x}{a-x}) dx =................ A) -a cos^(-1) (x/a) -...

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  5. intx^2e^(3x) dx=............ A) (1/3) x^2e^(3x) - (2/9) x e^(3x) + (2...

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  6. int tan^(-1)sqrt x dx=.............a)xtan^(-1)sqrt x - sqrt x + tan^(-...

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  7. int e^x frac{x}{(x+1)^2} dx =........... A) e^x(x+1) + c B) frac{e^x...

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  8. intfrac{x+1}{x^2 + 5x + 6} dx=............ A) log(x+2) +2 log(x+3) +...

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  9. intfrac{ t^2 + 1}{ t^4 + 1} dt=...........a) frac{1}{sqrt2}[tan^(-1)(s...

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  10. intfrac{1}{4+5 cos^2 x} dx=.............. A) (1/3)tan^(-1)((2/3)tan x...

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  11. intsin^(-1) x dx=............ A) x sin^(-1) x + sqrt (1-x^2) + c B) ...

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  12. int frac{e^(1/x)}{x^2} dx=........... A) frac{e^(1/x)}{x^2} + c B) 1...

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  13. int frac{dx}{1+e^(-x)} =........... A) log(1+e^(-x)) + c B) log(e^x ...

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  14. int sin^2 x cos^2 x dx=............. A) 1/8(x-frac{sin 4x}{4}) + c B...

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  15. int frac{1}{ 3 x- 2 sqrt x} dx=..........

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  16. intfrac{x^2 + 3x +5}{(x+2)(x^2 + 2x +3)} dx=............ (A) log (x+2...

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  17. Evaluate the following: inttan^2 x dx

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  18. Evaluate the following: int x root(3)(x) dx

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  19. Evaluate: int log x dx

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  20. Evaluate: int e^x (sin x+ cos x) dx

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