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Popular >

integral of (10+u)/u

Solution

\int \frac{10 + u}{u} d u

Solution

10 ln ∣ u ∣ + u + C

Solution steps

\int \frac{10 + u}{u} d u

Expand

\frac{10 + u}{u} : \frac{10}{u} + 1

= \int \frac{10}{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{10}{u} d u + \int 1 d u

\int \frac{10}{u} d u = 10 ln ∣ u ∣

\int 1 d u = u

= 10 ln ∣ u ∣ + u

Add a constant to the solution

= 10 ln ∣ u ∣ + u + C

Popular Examples

integral of 3/(sqrt(x))+(xsqrt(x))/4+C

\int \frac{3}{x} + \frac{x x}{4} + C d x

d/(dt)(10000-9000e^{-0.3t})

\frac{d}{d t} (10000 - 9000 e^{- 0.3 t})

integral of (x-1)/(x^2-x-1)

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

(\partial)/(\partial y)(7xy^6)

\frac{\partial}{\partial y} (7 x y^{6})

tangent of 3x^3-6x^2+4x+21 tangent of

3 x^{3} - 6 x^{2} + 4 x + 21

Frequently Asked Questions (FAQ)

What is the integral of (10+u)/u ?
The integral of (10+u)/u is 10ln|u|+u+C