Prove that : `loge.(1+3x+2x^2)=3x-5/2x^2+9/3x^3-17/4x^4+…,|x|lt1/2`

Evaluate the following lim_(xto1) (1+2x-3x^2+4x^3-5x^4)

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))= tan^(-1)2x,|2x| lt (1)/(sqrt(3)) .

Prove that int_0^(pi//4) cos^2 2x sin^3 4x dx=1/6

Evaluate the following lim_(xto0) (3x^2 +4x -1) (x^4+2x^3-3x^2 +5x+2)

Prove that: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))

Integrate the following int(x^4-3x^2+1)^4(2x^3-3x)dx

Differentiate. In (4x^2(2x-7)^3)/(3x^2-7)^5

Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

Evaluate the following: lim_(xtoinfty)(3x^2+x-1)/(2x^2-7x+5)

lim_(xto1)|x^2-3x+2|/(x^2-3x+2)