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Popular >

integral of ((1+y))/y

Solution

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

Solution

ln ∣ y ∣ + y + C

Solution steps

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

Expand

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

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

\int \frac{1}{y} d y = ln ∣ y ∣

\int 1 d y = y

= ln ∣ y ∣ + y

Add a constant to the solution

= ln ∣ y ∣ + y + C

Graph

Popular Examples

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\int_{0}^{l n (2)} e^{x} - 1 d x

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(\partial)/(\partial x)(x/((x^2+y^2+z^2)))

\frac{\partial}{\partial x} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} )})

y^{''}-xy^'+y=0

y^{^{''}} - x y^{^{'}} + y = 0

Frequently Asked Questions (FAQ)

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