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Popular >

integral of (5+x)/x

Solution

\int \frac{5 + x}{x} d x

Solution

5 ln ∣ x ∣ + x + C

Solution steps

\int \frac{5 + x}{x} d x

Expand

\frac{5 + x}{x} : \frac{5}{x} + 1

= \int \frac{5}{x} + 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{5}{x} d x + \int 1 d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 1 d x = x

= 5 ln ∣ x ∣ + x

Add a constant to the solution

= 5 ln ∣ x ∣ + x + C

Popular Examples

integral of csc^2(x)-1

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

integral of e^{(1+n)x}

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

integral of (sqrt(x))/(x+1)

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

tangent of f(x)=sqrt(3x+1),\at x=8 tangent of

f (x) = 3 x + 1, at x = 8

integral of 3sqrt(1-x^2)

\int 3 1 - x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of (5+x)/x ?
The integral of (5+x)/x is 5ln|x|+x+C