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Popular >

integral of (y+1)/y

Solution

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

Solution

y + ln ∣ y ∣ + C

Solution steps

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

Expand

\frac{y + 1}{y} : 1 + \frac{1}{y}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d y = y

\int \frac{1}{y} d y = ln ∣ y ∣

= y + ln ∣ y ∣

Add a constant to the solution

= y + ln ∣ y ∣ + C

Popular Examples

derivative of f(x)= 1/(x+2)derivative of

f (x) = \frac{1}{x + 2}

(\partial)/(\partial x)(x/(3+y))

\frac{\partial}{\partial x} (\frac{x}{3 + y})

integral of 1/(x^2+5x+4)

\int \frac{1}{x ^{2} + 5 x + 4} d x

limit as x approaches 5 of sqrt(x-9)

x \to 5 lim (x - 9)

partialfraction x/(2x+1)partial fractions

\frac{x}{2 x + 1}

Frequently Asked Questions (FAQ)

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