What is the integral of (4x^3+3^x) ?

The integral of (4x^3+3^x) is x^4+(3^x)/(ln(3))+C

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integral of (4x^3+3^x)

\int (4 x^{3} + 3^{x}) d x

x^{4} + \frac{3 ^{x}}{ln ( 3 )} + C

Solution steps

\int 4 x^{3} + 3^{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 4 x^{3} d x + \int 3^{x} d x

\int 4 x^{3} d x = x^{4}

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

= x^{4} + \frac{3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= x^{4} + \frac{3 ^{x}}{ln ( 3 )} + C

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

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

x, - x, 1, 4

sin (2 x)

\int x + \frac{x ^{2}}{2} + \frac{5 x ^{3}}{3} d x

What is the integral of (4x^3+3^x) ?
The integral of (4x^3+3^x) is x^4+(3^x)/(ln(3))+C