Math
posted by Vanessa .
Find the indefinite integral.
x^2(5 x^3 + 9)^3 dx

I observed that the derivative of the inside of the bracket sits out front as a multiple of that.
If that is the case, I just reverse by "thinking"
if dy/dx = x^2(5x^3 + 9)^3
y = (x^2/(15x^2)) (5x^3 +9)^4 * (1/4)+ c
= (1/60) (5x^3 + 9)^4 + c 
Thanks Reiny for all your help, I really appreciate it.
Respond to this Question
Similar Questions

Calculus
Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of (sin(3*pi*t))dt For this one, I got 1/3pi cos (9 pi^2) + 1/3pi 2. indefinite integral of sinxcos(cosx)dx I got sin(cosx) + C 3. Indefinite integral of x over (root … 
Calculus II/III
A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the xaxis from 4 to 9. For part … 
Math
1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. Answer = + C 2. Evaluate the indefinite integral (12sin x+4tan x)dx. Answer = + C 3. Evaluate the indefinite integral. (x^7)e^(x^8)dx. Answer = + C Thank you … 
Calc BC
1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2(pix/7)dx 2. Find the indefinite integral by making the substitution x=3tan(theta). Indefinite integral x*sqrt(9+x^2)dx 3. Find the indefinite integral. Indefinite … 
Calculus
Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral. 
Indefinite Integrals
find the indefinite integral of (1/x)*(e^(2log[ 3,x])) dx where 3 is base of the log i cannot even figure out where to start :( please help. thank you 
math
Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6 
math
Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x 
Math
good day please help with this indefinite integral,especially what formula i can use to solve it2x+1/(3x^2+3x+5)dx.Find the indefinite integral. 
Math (Integrals)
Find the indefinite integral in two ways. ∫(2x1)^2 dx The first way I used was using the power rule and chain rule with substitution. Let u = 2x  1 du = 2 dx (1/2)∫ u^2 du (Applying power rule) (1/2) * (u^3/3) + C =(2x1)^3/6 …