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Popular >

integral of (7+u)/u

Solution

\int \frac{7 + u}{u} d u

Solution

7 ln ∣ u ∣ + u + C

Solution steps

\int \frac{7 + u}{u} d u

Expand

\frac{7 + u}{u} : \frac{7}{u} + 1

= \int \frac{7}{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{7}{u} d u + \int 1 d u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

\int 1 d u = u

= 7 ln ∣ u ∣ + u

Add a constant to the solution

= 7 ln ∣ u ∣ + u + C

Graph

Popular Examples

integral of x(1-7x^2)^6

\int x (1 - 7 x^{2})^{6} d x

integral of-0.6x+30

\int - 0.6 x + 30 d x

integral of (e^x)/((e^x+1)^{10)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{10}} d x

integral of 1/(a+x^2)

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

integral of e^xsqrt(47+e^x)

\int e^{x} 47 + e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (7+u)/u ?
The integral of (7+u)/u is 7ln|u|+u+C