`int(1+x^(5))/(1+x)dx" is equal to: ",[[" A) "1-x+x^(2)-x^(3)+x^(4)+c],[" B) "x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+(x^(5))/(5)+c],[" C) "(1+x)^(5)+c],[" D) "(1-x)^(5)+c]]`

Let S=x-(x^(3))/(3!)+(x^(5))/(5!) … and C=1-(x^(2))/(2!)+(x^(4))/(4!) Then,

int(x^(3))/(x+1)dx is equal to x+(x^(2))/(2)+(x^(3))/(3)-log|1-x|+C(b)x+(x^(2))/(2)-(x^(3))/(3)-log|1-x|+C(c)x-(x^(2))/(2)-(x^(3))/(3)-log|1+x|+C(d)x-(x^(2))/(2)+(x^(3))/(3)-log|1+x|+C

int(x+(1)/(x))^(3/2)((x^(2)-1)/(x^(2)))dx is equal to (A) (1)/(3)(x+(1)/(x))^(3)+C (B)(2)/(5)(x+(1)/(x))^(5/2)

int(x^(6)+1)/(x^(2)+1)dx is equal (x^(5))/(5)+(x^(3))/(3)+x+c(b)(x^(5))/(5)-(x^(3))/(3)=x+c(x^(5))/(5)-(x^(3))/(3)+(x^(2))/(2)+c(d)(x^(5))/(5)-(x^(3))/(3)+x+c

The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to: (1)(-x^(5))/((x^(5)+x^(3)+1)^(2))+C(2)(x^(5)x^(3))/(2(x^(5)+x^(3)+1)^(2))+C(3)(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C(4)(-x^(3)+x^(3))/(2(x^(5)+x^(3)+1)^(2))+C where C is an arbitrary constant.

int(x^(9))/((4x^(2)+1)^(6))dx is equal to (A) (1)/(5x)(4+(1)/(x^(2)))^(-5)+c(B)(1)/(5)(4+(1)/(x^(2)))^(-5)+c(C)(1)/(10x)(4x+1)^(-5)+c (D) (1)/(10)((1)/(x^(2))+4)^(-5)+c

int(x^(2)+3)/(x^(6)(x^(2)+1))dx=-(a)/(x)+(b)/(3x^(3))-(d)/(5x^(5))-2tan^(-1)x+c

If int(dx)/(x^(2)(x^(4)+1)^(3//4))=A((x^(4)+1)/(x^(4)))^(B)+c, then

The integral int(2x^(12)+5x^(9))/([x^(5)+x^(3)+1]^(3))*dx is equal to- (A) (x^(10))/(2(x^(5)+x^(3)+1)^(2))(B)(x^(5))/(2(x^(5)+x^(3)+1)^(2))(C)-(x^(10))/(2(x^(5)+x^(3)+1)^(2))(D)-(x^(5))/(2(x^(5)+x^(3)+1)^(2))

int e^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx is equal to (1)/(2)xe^(x^(2))e^(x^(4))+c( b) (1)/(2)x^(2)e^(x^(4))+c(1)/(2)e^(x^(2))e^(x^(4))+c(d)(1)/(2)x^(2)e^(x^(2))e^(x^(4))+c