If x^3 e^ 5 x d x= e^ 5 x 5^4 [f(x)]+C , then f(x) is equal to

Step-by-step solution

We have given that, x^3 e^ 5 x d x= e^ 5 x 5^4 [ (x) ]+c By using the method of intergration by parts, we get aligned & x^3 e^ 5 x d x=x^3 e^ 5 x d x- d x^3 d x e^ 5 x d x d x & = x^3 e^ 5 x 5 - 3 x^2 e^ 5 x 5 d x+C aligned By using the method of integration by parts, we get aligned & = x^3 e^ 5 x 5 - 3 5 x^2 e^ 5 x d x & + 3 5 d x^2 d x e^ 5 x d x d x+C & = x^3 e^ 5 x 5 - 3 x^3 e^ 5 x 25 + 6 25 x e^ 5 x d x & = x^3 e^ 5 x 5 - 3 x^3 e^ 5 x 25 + 6 x 25 e^ 5 x d x & - 6 25 d x d x e^ 5 x d x d x & = x^3 e^ 5 x 5 - 3