Resolved: "Evaluate the integral. ∫axx2−bxdx"

Harlen Pritchard

Answered question

2021-11-05

Evaluate the integral.

\int \frac{a x}{x^{2} - b x} d x

Dora

Skilled2021-11-06Added 98 answers

Step 1
The given integral

\int (\frac{a x}{x^{2} - b x}) d x

can be evaluated as,

\int (\frac{a x}{x^{2} - b x}) d x = \int (\frac{a x}{x (x - b)}) d x

= \int (\frac{a}{x - b}) d x

Put, x-b=t
Taking differential on both sides,
dx=dt
Step 2
So, the

\int (\frac{a}{x - b}) d x

becomes,

\int \frac{a}{t} d t = a \int \frac{d t}{t}

= a (\log | t | + C)

Replace t by x−b,

\int (\frac{a x}{x^{2} - b x}) d x = a (\log | x - b | + C)

Hence,

\int (\frac{a x}{x^{2} - b x}) d x = a (\log | x - b | + C)

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