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Popular >

integral of 4x+1/x

Solution

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

Solution

2 x^{2} + ln ∣ x ∣ + C

Solution steps

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

\int 4 x d x = 2 x^{2}

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x^{2} + ln ∣ x ∣

Add a constant to the solution

= 2 x^{2} + ln ∣ x ∣ + C

Popular Examples

integral of 2/(2+x^2)

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

y^{^{'}} = x \cdot y

(dy)/(dt)+y/t =2

\frac{d y}{d t} + \frac{y}{t} = 2

y^{''}+4y=tan(2x)

y^{^{''}} + 4 y = tan (2 x)

limit as x approaches pi/4 of cos(2x)

x \to \frac{π}{4} lim (cos (2 x))

Frequently Asked Questions (FAQ)

What is the integral of 4x+1/x ?
The integral of 4x+1/x is 2x^2+ln|x|+C