   Chapter 8.4, Problem 26E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 19-32, find the indefinite integral. ∫ 25 x 2 + 4 x 4   d x

To determine

To calculate: The indefinite integral 25x2+4x4dx.

Explanation

Given:

The indefinite integral 25x2+4x4dx.

Calculation:

Because 25x2+4 is of the form a2+x2, use the trigonometric solution 5x=2tanθ to solve it as shown in the figure.

The derivative of the above equation is;

5dx=2sec2θdθ

Therefore;

25x2+4x4dx=4tan2θ+22(25tanθ)425sec2θdθ=1254sec3θtan4θdθ=1254cosθsin4θdθ=1254cotθcosec3θdθ

Assume cosecθ=t

So;

dt=cosecθcotθdθ

The above indefinite integral can be written as;

1254cotθcosec3θdθ=

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