What is the integral of (x^22^x+x)/(x^2) ?

The integral of (x^22^x+x)/(x^2) is (2^x)/(ln(2))+ln|x|+C

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integral of (x^22^x+x)/(x^2)

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

\frac{2 ^{x}}{ln ( 2 )} + ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{x ^{2} \cdot 2 ^{x} + x}{x ^{2}} : 2^{x} + \frac{1}{x}

= \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 = \frac{2 ^{x}}{ln ( 2 )}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{2 ^{x}}{ln ( 2 )} + ln ∣ x ∣

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + ln ∣ x ∣ + C

\frac{d}{d x} (\frac{( 3 x ^{2} + 1 ) ^{3}}{( 2 x ^{2} - 1 ) ^{4}})

f^{^{'}} (x) = a^{2 x}

n = 1 \sum \infty (\frac{n - 2}{n})^{n}

\int (sin (2 u) - cos (3 u))^{(2)} d u

\frac{d}{d x} (- 3 x - 9)

What is the integral of (x^22^x+x)/(x^2) ?
The integral of (x^22^x+x)/(x^2) is (2^x)/(ln(2))+ln|x|+C