`int_0^1 (2x^2-3)^n xdx`

int_0^1 x^2e^xdx

int_0^1(2-3x+x^2)dx

Evaluate: int_0^1xtan^(-1)xdx

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to a. int_0^1x^(n-1)(1-x)^n dx b. int_1^2x^n(x-1)^(n-1)dx c. int_1^2x^(n-1)(1+x)^n dx d. int_0^1(1-x)^(n-1)dx

Prove that for ngt1 . int_0^1(cos^-1x)^ndx=n(pi/2)^(n-1)-n(n-1)int_0^1(cos^-1x)^(n-2)dx

int_0^1 (tan^-1x)/xdx-1/2int_0^(pi/2) t/sint dt has the value (A) -1 (B) 1 (C) 2 (D) 0

Find the value of int_0^1 2x^3-3x^2-x+1 3dxdot

IfI_1=int_0^1 2^(x^2)dx ,I_2=int_0^1 2^(x^3)dx ,I_3=int_1^2 2^(x^2)dx ,I_4=int_1^2 2^(x^3)dx , then which of the following is/are true?

int_-1^1 (sinx+x^2)/(3-|x|)dx= (A) 0 (B) 2int_0^1 sinx/(3-|x|)dx (C) 2int_0^1 x^2/(3-|x|)dx (D) 2int_0^1 (sinx+x^2)/(3-|x|)dx

The value of int_0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is