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ans

_{[ ]}

^{[ ]} dx/(3+4sinx)^2

find value of

_{[ ]}

^{[ ]} (x -x^3)^1/3

x^4

nitin62225

solve it yourself

Hint:

1) convert sin x into tan(x/2)---------as sin (x)= 2tan(x/2)/sec²(x/2)

2)take x³ common from the numerator ,it will become x outside the bracket. divide the denom. by x u'll get x^3 in denominator. put num. as t and u'll get the denominator *(constt) = d/dx (t)

elessar_iitkgp

1)

{1/[3+(8tan(x/2) / (1+tan²(x/2))]} dx

{sec²(x/2)/[3+3tan²(x/2)+(8tan(x/2) ]} dx
Substitute tan(x/2) = t
2

{1/[3+3t²+8t]} dt
(2/3)

{1/[t²+ 8t/3 + 1]} dt
(2/3)

{1/[(t + 2/

3)²- (1/

3)²]} dt
(2/3)(1/2

3)ln[(

3t + 3)/(

3t + 1)]
(1/3

3)ln[(

3tan(x/2) + 3)/(

3tan(x/2) + 1)]

TRANSLTR

+ C....lol

Moderator

one ques at a time for the experts please ..

prasad_aspirant

can u tell me how to get that integral sign typed on keyboard

amar.gupta

very good work nitin62225 .

Dear, I think you have got the ans. of both of your questions.

however if doubt any please feel free to ask.

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