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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

Popular Examples

integral of x/(x^3-3x+2)

\int \frac{x}{x ^{3} - 3 x + 2} d x

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\int 5^{x} cos (x) d x

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\int tan (- x) d x

integral of (sqrt(16x^2-1))/(x^3)

\int \frac{16 x ^{2} - 1}{x ^{3}} d x

integral of 2e^x+x^2

\int 2 e^{x} + 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