Solution Found!
If you do not know what substitution to make, try reducing
Chapter 5, Problem 67E(choose chapter or problem)
If you do not know what substitution to make, try reducing the integral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68.
\(\int \frac{18 \tan ^{2} x \sec ^{2} x}{\left(2+\tan ^{3} x\right)^{2}} d x\)
a. \(u=\tan x\), followed by \(v=u^{3}\), then by \(w=2+v\)
b. \(u=\tan ^{3} x\), followed by \(v=2+u\)
c. \(u=2+\tan ^{3} x\)
Equation Transcription:
Text Transcription:
Integral 18 tan^2 x sec^2x/(2+tan^3 x)^2 dx
u=tan x
v=u^3
w=2+v
u=tan^3x
v=2+u
u=2+tan^3x
Questions & Answers
QUESTION:
If you do not know what substitution to make, try reducing the integral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68.
\(\int \frac{18 \tan ^{2} x \sec ^{2} x}{\left(2+\tan ^{3} x\right)^{2}} d x\)
a. \(u=\tan x\), followed by \(v=u^{3}\), then by \(w=2+v\)
b. \(u=\tan ^{3} x\), followed by \(v=2+u\)
c. \(u=2+\tan ^{3} x\)
Equation Transcription:
Text Transcription:
Integral 18 tan^2 x sec^2x/(2+tan^3 x)^2 dx
u=tan x
v=u^3
w=2+v
u=tan^3x
v=2+u
u=2+tan^3x
ANSWER:
Solution
Step 1 of 4
In this problem we have to evaluate the indefinite integral.
Given that
(a) given the substitution