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The value of integral inte^x(1/(sqrt(1+x...

The value of integral `inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi se q u a lto` `e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c` `e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c` `e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c` none of these

A

` e^(x)((1)/(sqrt(1+x^(2)))+(x)/(sqrt((1+x^(2))^(3))))+c`

B

` e^(x)((1)/(sqrt(1+x^(2)))-(x)/(sqrt((1+x^(2))^(3))))+c`

C

` e^(x)((1)/(sqrt(1+x^(2)))+(x)/(sqrt((1+x^(2))^(5))))+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
` int e^(x)((1)/(sqrt(1+x^(2)))-(x)/(sqrt((1+x^(2))^(3)))+(x)/(sqrt((1+x^(2))^(3)))+(1-2x^(2))/(sqrt((1+x^(2))^(5))))`
` = e^(x)(1)/(sqrt(1+x^(2)))+e^(x)(x)/(sqrt((1+x^(2))^(3)))=e^(x)((1)/(sqrt(1+x^(2)))+(x)/(sqrt((1+x^(2))^(3))))+C`
Using ` int e^(x)(f(x)+f'(x))dx, " we get " e^(x)f(x)+c`
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