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Single Variable Calculus

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Difficult

Integration by Parts: Power of $x$ and an Exponential

SVCALC-GB0J50

Evaluate the integral:

$$\int x^2 10^x dx$$

A

$= \cfrac{x^210^x}{\ln10} - \cfrac{2x 10^x }{\ln^210} + \cfrac{2 \cdot 10^x}{\ln^3 10} +C $

B

$= \cfrac{x^210^x}{\ln10} - \cfrac{2x 10^x }{\ln^210} - \cfrac{2 \cdot 10^x}{\ln^2 10} +C $

C

$= \cfrac{x^210^x}{\ln10} + \cfrac{2x 10^x }{\ln10} + \cfrac{2 \cdot 10^x}{\ln 10} +C $

D

$x^3 10^x-x^2 10^{x+1}+C$