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Popular >

integral of 1/(y+8)

Solution

\int \frac{1}{y + 8} d y

Solution

ln ∣ y + 8 ∣ + C

Solution steps

\int \frac{1}{y + 8} d y

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = y + 8

= ln ∣ y + 8 ∣

Add a constant to the solution

= ln ∣ y + 8 ∣ + C

Popular Examples

integral of (4x)/((x-3)(x+2))

\int \frac{4 x}{( x - 3 ) ( x + 2 )} d x

integral of (x^2)/((x+2)^2(x-3)^2)

\int \frac{x ^{2}}{( x + 2 ) ^{2} ( x - 3 ) ^{2}} d x

integral of (5x^3+2x^2+x)

\int (5 x^{3} + 2 x^{2} + x) d x

integral of cot^3(3x)csc^2(3x)

\int cot^{3} (3 x) csc^{2} (3 x) d x

integral of 6.4e^{(-3x+6)}

\int 6.4 e^{(- 3 x + 6)} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(y+8) ?
The integral of 1/(y+8) is ln|y+8|+C