What is the integral of (3y^2)/(x-5) ?

The integral of (3y^2)/(x-5) is 3y^2ln|-5+x|+C

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integral of (3y^2)/(x-5)

\int \frac{3 y ^{2}}{x - 5} d x

3 y^{2} ln ∣ - 5 + x ∣ + C

Solution steps

\int \frac{3 y ^{2}}{x - 5} d x

Take the constant out:

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

= 3 y^{2} \cdot \int \frac{1}{- 5 + x} d x

Apply u-substitution

: \int \frac{1}{u} d u

= 3 y^{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 y^{2} ln ∣ u ∣

Substitute back

u = - 5 + x

= 3 y^{2} ln ∣ - 5 + x ∣

Add a constant to the solution

= 3 y^{2} ln ∣ - 5 + x ∣ + C

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What is the integral of (3y^2)/(x-5) ?
The integral of (3y^2)/(x-5) is 3y^2ln|-5+x|+C