`int_(0)^(1) n^(2) x (1-x^(2))^ndx`

int_(0)^(1)tan^(-1)(1-x+x^(2))dx=

int_(0)^(1)x^(2)sqrt(1-x^(2))dx=

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)^(1) x^(2)/(x^(2)+1)dx=

evaluate int_(0)^(1)x^(2)(1-x)^(n)dx

int_(0)^(1)(2-x^(2))/(1+x^(2))dx=

int_(0)^(1)(2x)/((1+x^(2)))dx

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

int_(0)^(x)tan^(-1)(1-x+x^(2))dx