"Evaluate the indefinite integral. (Remember to use absolute..." solved and explained

Lorenzolaji

Answered question

2021-12-05

Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

\int \frac{d x}{q x + s} (q \neq 0)

navratitehf

Beginner2021-12-06Added 20 answers

Step 1
Given,

\int \frac{d x}{q x + s} (q \neq 0)

Step 2
Now integrating by substitution:
Put u=qx+s
differentiating with respect to x, we get

\frac{d u}{d x} = q (1) + 0 = q [∵ \frac{d}{d x} (x^{n}) = n x^{n - 1}]

\Rightarrow d x = \frac{d u}{q}

∴ \int \frac{d x}{q x + s} = \int \frac{d \frac{u}{q}}{u} = \frac{1}{q} \ln (u) + C [∵ \int \frac{1}{x} d x = \ln (x) + C]

Now replacing u=qx+s

∴ \int \frac{d x}{q x + s} = \frac{1}{q} \ln (q x + s) + C

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