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Popular >

integral of x/(x+

Solution

\int \frac{x}{x + d} d x

Solution

- d ln ∣ x + d ∣ + x + C

Solution steps

\int \frac{x}{x + d} d x

\frac{x}{x + d} = - \frac{d}{x + d} + 1

= \int - \frac{d}{x + d} + 1 d x

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{d}{x + d} d x + \int 1 d x

\int \frac{d}{x + d} d x = d ln ∣ x + d ∣

\int 1 d x = x

= - d ln ∣ x + d ∣ + x

Add a constant to the solution

= - d ln ∣ x + d ∣ + x + C

Popular Examples

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

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

y^{^{'''}} = 0

inverse oflaplace 4/(5s)inverse laplace

\frac{4}{5 s}

integral of (\sqrt[6]{x}+\sqrt[7]{x})

4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-5

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

Frequently Asked Questions (FAQ)

What is the integral of x/(x+ ?
The integral of x/(x+ is -dln|x+d|+x+C