How do you integrate #f(x)=x^2sinx# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer bp Feb 19, 2017 #int x^2 sin x dx= x^2 int sinx dx - int d/dx x^2 int sin x dx# =#-x^2 cos x-int 2x (-cos x)dx# =#-x^2 cos x +2int x cosx dx# = -#x^2 cos x+2[x int cos x dx- int d/dx x int cos x dx# =-#x^2 cosx+2[x sin x-int int cosxdx]# =# -x^2cos x +2x sin x +2cos x +C# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 1370 views around the world You can reuse this answer Creative Commons License