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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)=(e^x)/(x^2+6)derivative of

f (x) = \frac{e ^{x}}{x ^{2} + 6}

integral of (3x-1)/((x+4)^2)

\int \frac{3 x - 1}{( x + 4 ) ^{2}} d x

derivative of (sin(t)/(sqrt(1+x^2)))

\frac{d}{d x} (\frac{sin ( t )}{1 + x ^{2}})

integral of x^3e^{ax^4}

\int x^{3} e^{a x^{4}} d x

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

\int \frac{2 ( x ^{2} + 1 )}{x ( x ^{2} + 2 )} d x

Frequently Asked Questions (FAQ)

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