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Popular >

integral of (9+u)/u

Solution

\int \frac{9 + u}{u} d u

Solution

9 ln ∣ u ∣ + u + C

Solution steps

\int \frac{9 + u}{u} d u

Expand

\frac{9 + u}{u} : \frac{9}{u} + 1

= \int \frac{9}{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{9}{u} d u + \int 1 d u

\int \frac{9}{u} d u = 9 ln ∣ u ∣

\int 1 d u = u

= 9 ln ∣ u ∣ + u

Add a constant to the solution

= 9 ln ∣ u ∣ + u + C

Popular Examples

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\int \frac{u}{u ^{2} - 1} d u

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f(x)=6sin(2x)-3cos(3x)

f (x) = 6 sin (2 x) - 3 cos (3 x)

y^{^{''}} - y = t e^{t}

derivative of sqrt(2x)+\sqrt[3]{3x}

Frequently Asked Questions (FAQ)

What is the integral of (9+u)/u ?
The integral of (9+u)/u is 9ln|u|+u+C