I: int (1-x^(4))/(1-x)dx= x+(x^(2))/(2)+...

`I: int (1-x^(4))/(1-x)dx= x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+c`
II : `int 1+x+(x^(2))/(2!)+(x^(3))/(3!)+.....dx= e^(x)+c`

only I is true

only II is true

both I and II are true

neither I nor II true

Verified by Experts

The correct Answer is:

INDEFINITE INTEGRATION
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INDEFINITE INTEGRATION
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INDEFINITE INTEGRATION
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HYPERBOLIC FUNCTIONS
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INVERSE TRIGONOMETRIC FUNCTIONS
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int (x^(3))/(1+x^(4))dx=

`(1)/(4) log (1-x^(4)|+c`

`(1)/(2) log |1+x^(4)|+c`

`(1)/(4)log |1+x^(4)|+c`

none

`(x^(3))/(3)-x+"Tan"^(-1)x+c`

`(x^(5))/(5)+Tan^(-1)x+c`

`4x^(3)+Tan^(-1)x+c`

`(x^(4))/(4)+x+Tan^(-1)x+c`

`(1)/(2sqrt(2))Tan^(-1)((x^(2)+1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)-sqrt(2)x+1)/(x^(2)+sqrt(2)x+1)|+c`

`(1)/(2sqrt(2))Tan^(-1)((x^(2)\1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)+sqrt(2)x+1)/(x^(2)-sqrt(2)x+1)|+c`

`(1)/(2sqrt(2))Tan^(-1)((x^(2)\1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)-sqrt(2)x+1)/(x^(2)+sqrt(2)x+1)|+c`

none