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Popular >

integral of (y+4)/y

Solution

\int \frac{y + 4}{y} d y

Solution

y + 4 ln ∣ y ∣ + C

Solution steps

\int \frac{y + 4}{y} d y

Expand

\frac{y + 4}{y} : 1 + \frac{4}{y}

= \int 1 + \frac{4}{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{4}{y} d y

\int 1 d y = y

\int \frac{4}{y} d y = 4 ln ∣ y ∣

= y + 4 ln ∣ y ∣

Add a constant to the solution

= y + 4 ln ∣ y ∣ + C

Graph

Popular Examples

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\int_{0}^{2} π (4 x)^{2} d x

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\int \frac{1}{169 + x ^{2}} d x

(\partial)/(\partial x)(x^2ln(y)+5xy^3)

\frac{\partial}{\partial x} (x^{2} ln (y) + 5 x y^{3})

derivative of x^2sqrt(8x-1)derivative of

x^{2} 8 x - 1

derivative of (1-2x)/(4+x)derivative of

\frac{1 - 2 x}{4 + x}

Frequently Asked Questions (FAQ)

What is the integral of (y+4)/y ?
The integral of (y+4)/y is y+4ln|y|+C