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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 sqrt(81x^2+35)

\int 81 x^{2} + 35 d x

integral of (x+4)(x-7)

\int (x + 4) (x - 7) d x

integral of 15x^3cos(5x^4+11)

\int 15 x^{3} cos (5 x^{4} + 11) d x

integral of x(-cos(x)+1)

\int x (- cos (x) + 1) d x

integral of (3-4x)^7

\int (3 - 4 x)^{7} 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