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

int_0^1 x^2e^xdx

int_(0)^(1)2xdx

int_0^(pi/2)sin^2xdx =

If v_n=int_0^1x^n tan^-1xdx , show that: (n+1)u_n+(n-1)u_(n-2)=pi/2-1/n

int_ (0) ^ (pi) e ^ (sin ^ (2x)) cos ^ (3) xdx

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then

int_(0)^(1)(tan^(-1)xdx)/((1+x^(2))^((3)/(2)))

If 2int_(0)^(1) tan^(-1)xdx=int_(2)^(1)cot^(-1)(1-x+x^(2))dx . Then int_(0)^(1) tan^(-1)(1-x+x^(2))dx is equal to

int_ (0) ^ (pi) sin ^ (2) x cos ^ (3) xdx

int_(0)^( pi/2)x sin xdx