Find the indefinite integral. |x(1 – 3x²)+ dx

Answered: |x(1 – 3x²)+ dx

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 2E

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Question

Find the indefinite integral.

Expert Solution

Step 1

Given: $\int x {(1 - 3 x^{2})}^{4} d x$

for evaluating this limit we substitute

$1 - 3 x^{2} = t$

now differentiating it both side with respect to $t$

$\begin{array}{rcl} 0 - 3 (2 x) \frac{d x}{d t} & = & 1 (∵ \frac{d}{d x} (k x^{2}) = k (2 x)) \\ - 6 x \frac{d x}{d t} & = & 1 \\ x d x & = & - \frac{d t}{6} \end{array}$

now replacing $x d x$ with $- \frac{d t}{6}$ and $(1 - 3 x^{2})$ with $t$ in given integral

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