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Popular >

integral of 2x^{-1}+5

Solution

\int 2 x^{- 1} + 5 d x

Solution

2 ln ∣ x ∣ + 5 x + C

Solution steps

\int 2 x^{- 1} + 5 d x

2 x^{- 1} = \frac{2}{x}

= \int \frac{2}{x} + 5 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{2}{x} d x + \int 5 d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 5 d x = 5 x

= 2 ln ∣ x ∣ + 5 x

Add a constant to the solution

= 2 ln ∣ x ∣ + 5 x + C

Graph

Popular Examples

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\int \frac{16}{25 + 9 x ^{2}} d x

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

integral of 5x*ln(3-x)

\int 5 x \cdot ln (3 - x) d x

integral of 4/3 x^{3/2}

\int \frac{4}{3} x^{\frac{3}{2}} d x

integral of (sec^2(pis))/(tan(pis))

\int \frac{sec ^{2} ( π s )}{tan ( π s )} d s

Frequently Asked Questions (FAQ)

What is the integral of 2x^{-1}+5 ?
The integral of 2x^{-1}+5 is 2ln|x|+5x+C