What is the integral of (3x^2-4*5^x) ?

The integral of (3x^2-4*5^x) is x^3-(4*5^x)/(ln(5))+C

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integral of (3x^2-4*5^x)

\int (3 x^{2} - 4 \cdot 5^{x}) d x

x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )} + C

Solution steps

\int 3 x^{2} - 4 \cdot 5^{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 3 x^{2} d x - \int 4 \cdot 5^{x} d x

\int 3 x^{2} d x = x^{3}

\int 4 \cdot 5^{x} d x = \frac{4 \cdot 5 ^{x}}{ln ( 5 )}

= x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )}

Add a constant to the solution

= x^{3} - \frac{4 \cdot 5 ^{x}}{ln ( 5 )} + C

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What is the integral of (3x^2-4*5^x) ?
The integral of (3x^2-4*5^x) is x^3-(4*5^x)/(ln(5))+C