Find an antiderivative of the given function.
-$x \sqrt { 2 } + 5 ^ { - x }$
A) $\frac { x \sqrt { 2 } - 1 } { \sqrt { 2 } - 1 } - \frac { 5 ^ { - x } } { \ln 5 }$
B) $\frac { x \sqrt { 2 } + 1 } { \sqrt { 2 } + 1 } - \frac { 5 ^ { - x } } { \ln 5 }$
C) $\frac { x \sqrt { 2 } } { \sqrt { 2 } + 1 } - \frac { 5 ^ { - x } } { \ln 5 }$
D) $\frac { x \sqrt { 2 } + 1 } { \sqrt { 2 } + 1 } + \frac { 5 ^ { - x } } { \ln 5 }$

Question

Quizplus · Accepted Answer

The antiderivative of $x\sqrt{2}$ is $\frac{x^2\sqrt{2}}{2}$, which can be rewritten as $\frac{x\sqrt{2}}{\sqrt{2}+1}$ after integrating. The antiderivative of $5^{-x}$ is $-\frac{5^{-x}}{\ln 5}$, but since it's subtracted in the options, it becomes $-\frac{5^{-x}}{\ln 5}$. Option B correctly combines these results.

Find an Antiderivative of the Given Function x2+5−xx \sqrt { 2 } + 5 ^ { - x }x2​+5−x

Find an Antiderivative of the Given Function $x \sqrt { 2 } + 5 ^ { - x }$