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int e^(x)((2+sin 2x)/(1+cos 2x)dx=...

`int e^(x)((2+sin 2x)/(1+cos 2x)dx=`

A

`e^(x) cotx +c`

B

`2e^(x) sec^(2) x+c`

C

`e^(x)cos 2x+c`

D

`e^(x) tan x +c`

Text Solution

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The correct Answer is:
D
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SIA PUBLICATION-INDEFINITE INTEGRATION -PROBLEMS
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  2. If int((x^(2)-1))/((x+1)^(2)sqrt(x(x^(2)+x+1)))dx=ATan^(-1)(sqrt(x^(2+...

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  3. int e^(x)((2+sin 2x)/(1+cos 2x)dx=

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  4. int(x-sinx)/(1+cosx)dx= tan((x)/(2))+plog|sec((x)/(2))|+c rArr p=

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  5. int (dx)/(x(logx-2)(logx-3))=I+c rArr I=

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  6. int (dx)/(x^(2)sqrt(4+x^(2)))=

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  7. If int sec^(2) x "cosec"^(4) x dx =-1/3 cos^(3)x + k tanx - 2cot x+c, ...

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  8. int (dx)/(sqrt(x-x^(2)))=

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  9. int(sqrt((a+x)/(a-x))) + sqrt((a-x)/(a+x))dx is equal to

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  10. If int (sin^(8)x-cos^(8)x)/(1-2sin^(2)cos^(2)x)dx=A sin 2x+B, then A=

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  11. int (1+cos4x)/(cotx-tanx)dx=

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  12. int (7x^(8)+8x^(7))/((1+x+x^(8))^(2))dx=f(x)+c rArr f(x)=

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  13. If f(n)(x) = log log…..log x(log is repeated n-times), then int (xf(1)...

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  14. int (1-cosx)"cosec"^(2)x dx=f(x)+c rArr f(x)=

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  15. int (dx)/((x+1)sqrt(4x+3))=

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  16. int(2-sin 2x)/(1-cos2x)e^(x) dx is equal to

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  17. If I(n) = int(sin^(n))dx, then nI(n)-(n-1)I(n-1) equals to

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  18. If int(e^(x))(1-sinx)/(1-cosx)dx=f(x) constant, then f(x) is equal to

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  19. If I(n)= intx^(n) e^(cx) dx for n ge 1, then c, I(n) + nI(n-1) is equa...

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  20. If inte^(x)(1+x) sec^(2)(xe^(x))dx = f(x) + constant, then f(x) is equ...

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