Let `P(x)` be a polynomial function satisfying `P(x)-P'(x)=x^(2)+2x+1`.The value of definite integral `int_0^1(1)/(p(x))dx` is equal to

The value of the definite integral int_0^(pi/2) ((1+sin3x)/(1+2sinx)) dx equals to

Evaluate the definite integrals int_0^1 (dx)/(1-x^2)

The value of the definite integral int_(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)dx equals

Evaluate the definite integrals int_0^1(2x+3)/(5x^2+1)dx

Evaluate the definite integrals int_0^1(2x+3"")/(5x^2+1)dx

The value of definite integral int _(0)^(oo) (dx )/((1+ x^(9)) (1+ x^(2))) equal to:

Let f(x) be a function satisfying f'(x)=f(x) with f(0) =1 and g(x) be a function that satisfies f(x) + g(x) = x^2 . Then the value of the integral int_0^1f(x) g(x) dx , is

Evaluate the following definite integral: int_0^1 1/(2x^2+x+1)dx

Let f(x)=int _( x )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integral int _(0)^(2) xf (x ) dx is equal to:

Let p (x) be a polynomial with real coefficient and p (x)-p'(x) =x^(2)+2x+1. Find P (-1).