( x)^2 x^3 d x= x^4 32 f(x)+C f(x)=

Step-by-step solution

I= ( x)^2 x^3 d x Using integration by parts, I=( x)^2 x^3 d x- ( d( x)^2 d x x^3 d x ) d x aligned & = ( x)^2 x^4 4 - 2 x x x^4 4 d x & = ( x)^2 x^4 4 - 1 2 ( x) x^3 d x & = ( x)^2 x^4 4 - 1 2 aligned [( x) x^3 d x- ( d x d x x^3 d x ) d x ] aligned & = ( x)^2 x^4 4 - 1 2 [ ( x) x^4 4 - 1 x x^4 4 d x ] & = ( x)^2 x^4 4 - 1 8 ( x) x^4+ 1 8 x^4 4 +C & = x^4 32 [8( x)^2-4( x)+1 ]+C aligned f(x)=8( x)^2-4( x)+1