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Popular >

integral of 1+1/y

Solution

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

Solution

y + ln ∣ y ∣ + C

Solution steps

\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

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

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

laplacetransform e^{(2t)}laplace transform

e^{(2 t)}

integral of 1/(sqrt(x^2+10x))

\int \frac{1}{x ^{2} + 10 x} d x

(dy}{dx}=-\frac{(e^x))/8

\frac{d y}{d x} = - \frac{( e ^{x} )}{8}

integral of-2e^{2t}

\int - 2 e^{2 t} d t

Frequently Asked Questions (FAQ)

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