What is the integral of ((x+3)/(2^x)-sqrt(3)) ?

The integral of ((x+3)/(2^x)-sqrt(3)) is -x/(ln(2)*2^x)-1/(ln^2(2)*2^x)-3/(ln(2)*2^x)-sqrt(3)x+C

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

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

- \frac{x}{ln ( 2 ) \cdot 2 ^{x}} - \frac{1}{ln ^{2} ( 2 ) \cdot 2 ^{x}} - \frac{3}{ln ( 2 ) \cdot 2 ^{x}} - 3 x + C

Solution steps

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

\int \frac{x + 3}{2 ^{x}} d x = - \frac{x}{ln ( 2 ) \cdot 2 ^{x}} - \frac{1}{ln ^{2} ( 2 ) \cdot 2 ^{x}} - \frac{3}{ln ( 2 ) \cdot 2 ^{x}}

\int 3 d x = 3 x

= - \frac{x}{ln ( 2 ) \cdot 2 ^{x}} - \frac{1}{ln ^{2} ( 2 ) \cdot 2 ^{x}} - \frac{3}{ln ( 2 ) \cdot 2 ^{x}} - 3 x

Add a constant to the solution

= - \frac{x}{ln ( 2 ) \cdot 2 ^{x}} - \frac{1}{ln ^{2} ( 2 ) \cdot 2 ^{x}} - \frac{3}{ln ( 2 ) \cdot 2 ^{x}} - 3 x + C

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

x^{4} e^{6 x}

\frac{d ^{3} y}{d x ^{3}} + \frac{d ^{2} y}{d x ^{2}} - 2 y = 0

\int cos (n) x d x

y = 2 x^{3} - x^{2} + \frac{4}{x}, (4, 1)

What is the integral of ((x+3)/(2^x)-sqrt(3)) ?
The integral of ((x+3)/(2^x)-sqrt(3)) is -x/(ln(2)*2^x)-1/(ln^2(2)*2^x)-3/(ln(2)*2^x)-sqrt(3)x+C