What is the integral of 1/(6y) ?

The integral of 1/(6y) is 1/6 ln|y|+C

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integral of 1/(6y)

\int \frac{1}{6 y} d y

\frac{1}{6} ln ∣ y ∣ + C

Solution steps

\int \frac{1}{6 y} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= \frac{1}{6} ln ∣ y ∣

Add a constant to the solution

= \frac{1}{6} ln ∣ y ∣ + C

\int \frac{1}{49 + t ^{2}} d t

y = sin (x), at x = \frac{7 π}{6}

x \to 0.9 lim (2 x^{2} - 5 x + 1)

\int - \frac{x}{x + 1} d x

f (x) = \frac{1}{x ^{6}}, (- 2, \frac{1}{64})