What is the integral of 4x^{1/2}+2e^x+3^x-3 ?

The integral of 4x^{1/2}+2e^x+3^x-3 is 8/3 x^{3/2}+2e^x+(3^x)/(ln(3))-3x+C

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integral of 4x^{1/2}+2e^x+3^x-3

\int 4 x^{\frac{1}{2}} + 2 e^{x} + 3^{x} - 3 d x

\frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x + C

Solution steps

\int 4 x^{\frac{1}{2}} + 2 e^{x} + 3^{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 4 x^{\frac{1}{2}} d x + \int 2 e^{x} d x + \int 3^{x} d x - \int 3 d x

\int 4 x^{\frac{1}{2}} d x = \frac{8}{3} x^{\frac{3}{2}}

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

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

\int 3 d x = 3 x

= \frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x + C

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\int (x + 1) \cdot e^{3 x + 1} d x

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

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

What is the integral of 4x^{1/2}+2e^x+3^x-3 ?
The integral of 4x^{1/2}+2e^x+3^x-3 is 8/3 x^{3/2}+2e^x+(3^x)/(ln(3))-3x+C