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Popular >

integral of (2x+1/x)

Solution

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

Solution

x^{2} + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= x^{2} + ln ∣ x ∣

Add a constant to the solution

= x^{2} + ln ∣ x ∣ + C

Graph

Popular Examples

integral of x^7(x^4+1)^{10}

\int x^{7} (x^{4} + 1)^{10} d x

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\int 16 - (x - 1)^{2} d x

integral of (9^x-12e^x-5sin(x)+8)

\int (9^{x} - 12 e^{x} - 5 sin (x) + 8) d x

integral of (x)e^x

\int (x) e^{x} d x

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

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

Frequently Asked Questions (FAQ)

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