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Popular >

integral of (3+u)/u

Solution

\int \frac{3 + u}{u} d u

Solution

3 ln ∣ u ∣ + u + C

Solution steps

\int \frac{3 + u}{u} d u

Expand

\frac{3 + u}{u} : \frac{3}{u} + 1

= \int \frac{3}{u} + 1 d u

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{3}{u} d u + \int 1 d u

\int \frac{3}{u} d u = 3 ln ∣ u ∣

\int 1 d u = u

= 3 ln ∣ u ∣ + u

Add a constant to the solution

= 3 ln ∣ u ∣ + u + C

Popular Examples

y^{''}+6y^'+34y=0,y(0)=4,y^'(0)=-11

y^{^{''}} + 6 y^{^{'}} + 34 y = 0, y (0) = 4, y^{^{'}} (0) = - 11

x^3y^'+3x^2y= 1/x

x^{3} y^{^{'}} + 3 x^{2} y = \frac{1}{x}

integral of (5/(x^8)-7/(\sqrt[4]{x^3)})

derivative of \sqrt[4]{8x^2}

derivative of 5x^2sin(x+4x)

\frac{d}{d x} (5 x^{2} sin (x) + 4 x)

Frequently Asked Questions (FAQ)

What is the integral of (3+u)/u ?
The integral of (3+u)/u is 3ln|u|+u+C