How do you evaluate the integral int x^3e^(x^2)"d"x? Calculus Techniques of Integration Integration by Parts 1 Answer Harish Chandra Rajpoot Jun 21, 2018 \int x^3e^{x^2}\ dx=1/2(x^2-1)e^{x^2}+C Explanation: Let x^2=t\implies 2x=dt\ or \ xdx=\frac{dt}{2} \therefore \int x^3e^{x^2}\ dx =\int x^2e^{x^2}(xdx) =\int te^t\frac{dt}{2} =\frac{1}{2}\int te^t\ dt =\1/2(t\int e^t \dt-\int (\frac{d}{dt}(t)\cdot \int e^t\ dt)dt) =\1/2(te^t-\int (1\cdot e^t)dt) =\1/2(te^t-\int e^tdt) =\1/2(te^t-e^t)+C =\1/2(t-1)e^t+C =1/2(x^2-1)e^{x^2}+C Answer link Related questions How do I find the integral int(x*ln(x))dx ? How do I find the integral int(cos(x)/e^x)dx ? How do I find the integral int(x*cos(5x))dx ? How do I find the integral int(x*e^-x)dx ? How do I find the integral int(x^2*sin(pix))dx ? How do I find the integral intln(2x+1)dx ? How do I find the integral intsin^-1(x)dx ? How do I find the integral intarctan(4x)dx ? How do I find the integral intx^5*ln(x)dx ? How do I find the integral intx*2^xdx ? See all questions in Integration by Parts Impact of this question 7078 views around the world You can reuse this answer Creative Commons License