   Chapter 4.R, Problem 24E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ x + 2 x 2 + 4 x   d x

To determine

To evaluate:

x+2x2+4xdx if it exists

Explanation

1) Concept:

By using the substitution rule

2) Theorem:

Substitution rule:

If u=g(x) is a differentiable function whose range is an interval I, and f is continuous on the I, then

f(gx)g'xdx=fudu

3) Formula:

xndx=xn+1 n+1+C

4) Given:

x+2x2+4xdx

5) Calculation:

Consider, x+2x2+4xdx

By applying substitution rule for indefinite integrals,

Let u=x2+4x

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