How do you integrate {x(sqrt(1+x^2)} dx{x(√1+x2}dx from 0 to 1? Calculus Introduction to Integration Integrals of Polynomial functions 1 Answer Ratnaker Mehta Sep 22, 2016 I=1/3(2sqrt2-1)I=13(2√2−1). Explanation: Let I=int_0^1 {xsqrt(1+x^2)}dx.I=∫10{x√1+x2}dx. We subst. 1+x^2=t^2 rArr 2xdx=2tdt, i.e., xdx=tdt1+x2=t2⇒2xdx=2tdt,i.e.,xdx=tdt Further, x=0 rArr t=1, and, x=1 rArr t=sqrt2x=0⇒t=1,and,x=1⇒t=√2. :. I=int_1^(sqrt2) t.tdt = int_1^(sqrt2) t^2dt=[t^3/3]_1^sqrt2. =1/3[sqrt2^3-1]. :. I=1/3(2sqrt2-1). Answer link Related questions How do you evaluate the integral intx^3+4x^2+5 dx? How do you evaluate the integral int(1+x)^2 dx? How do you evaluate the integral int8x+3 dx? How do you evaluate the integral intx^10-6x^5+2x^3 dx? What is the integral of a constant? What is the antiderivative of the distance function? What is the integral of |x|? What is the integral of 3x? What is the integral of 4x^3? What is the integral of sqrt(1-x^2)? See all questions in Integrals of Polynomial functions Impact of this question 45930 views around the world You can reuse this answer Creative Commons License