Key to "Evaluate the integrals: ∫xx2−25dx"

pavitorj6

Answered question

2021-12-06

Evaluate the integrals:

\int \frac{x}{x^{2} - 25} d x

Provere

Beginner2021-12-07Added 18 answers

Step 1
Given integral,

\int \frac{x}{x^{2} - 25} d x

Step 2
Let

I = \int \frac{x}{x^{2} - 25} d x

putting

u = x^{2} - 25

\frac{d u}{d x} = 2 x

\Rightarrow \frac{1}{2} d u = x d x

Now

I = \frac{1}{2} \int \frac{d u}{u}

= \frac{1}{2} \ln | u | + C

= \frac{1}{2} \ln | x^{2} - 25 | + C

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