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Popular >

integral of (4+1/x)

Solution

\int (4 + \frac{1}{x}) d x

Solution

4 x + ln ∣ x ∣ + C

Solution steps

\int 4 + \frac{1}{x} 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 4 d x + \int \frac{1}{x} d x

\int 4 d x = 4 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 4 x + ln ∣ x ∣

Add a constant to the solution

= 4 x + ln ∣ x ∣ + C

Popular Examples

integral of sqrt(5-16x^2)

\int 5 - 16 x^{2} d x

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

\int \frac{( x + 1 ) ^{2}}{x ( 1 + x ^{2} )} d x

integral of 2x^2+3x+1

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

integral of (cos(2x))/(sqrt(sin(2x)))

\int \frac{cos ( 2 x )}{sin ( 2 x )} d x

integral of 1/((2n+1)^3)

\int \frac{1}{( 2 n + 1 ) ^{3}}

Frequently Asked Questions (FAQ)

What is the integral of (4+1/x) ?
The integral of (4+1/x) is 4x+ln|x|+C