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For x ^ 2 ne n pi + 1, n in N ...

For ` x ^ 2 ne n pi + 1, n in N ` ( the set of natural numbers ), the integral ` int x sqrt ((2 sin (x ^ 2 - 1 ) - sin 2 (x ^ 2 - 1 ))/(2 sin ( x ^ 2 - 1 ) + sin2 (x ^ 2 - 1 ) )) dx ` is

A

`log|sec((x^(2)+1)/(2))|+c`

B

`log|sec((x^(2)+1)/(2))|+c`

C

`-log|tan((x^(2)+1)/(2))|+c`

D

`-log|cot((x^(2)+1)/(2))|+c`

Text Solution

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The correct Answer is:
A, B
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FIITJEE-INDEFINTE INTEGRAL-ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL-II)
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  10. int((1+x^(2))(2+x^2))/((xco sx+sinx)^(4))dx equals

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  11. int(dx)/((1+sqrt(x))^8)=

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  13. If int(sinx)/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+c then

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  14. If intxlog(1+x^(2))dx=A(x).log(1+x^(2))+B(x)+c, then

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  15. If int(sin3theta+sintheta)e^(sintheta)costhetad theta=(Asin^3theta+Bco...

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  16. If int((3x+4))/((x^(3)-2x-4))dx=Alog|x-2|+Blog(f(x))+c, then

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  18. If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Psqrt(1-9x^(2))+Q(cos^(-...

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  19. If int(dx)/(x^(22)(x^7-6))=A{ln(p)^6+9p^2-2p^3-18 p}+c, then

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