7. Antiderivatives & Indefinite Integrals

Which of the following is an antiderivative of $5^x$ with respect to $x$?

Which of the following is an antiderivative of $2x$?

Find a particular solution to the differential equation $\frac{dy}{dx}=2x$, given that $y\left(1\right)=5$.

Which of the following is an antiderivative of $2e^x$ with respect to $x$?

Which of the following is an antiderivative of $\frac{1}{x^2}$?

Which of the following is an antiderivative of $\cos x$?

Which of the following is an antiderivative of $f\left(x\right)=\cos (x^2-5)$?

Which of the following is an antiderivative of $f\left(x\right)=1+x^3$?

Which of the following is an antiderivative of the function $f\left(x\right)=\cos x$?

29–62. Integrals Evaluate the following integrals. Include absolute values only when needed.

∫ e^{2x} / (4 + e^{2x}) dx

Find the antiderivative of the following function.

$f\left(x\right)=200$

If $F\left(x\right)$ and $G\left(x\right)$ are both antiderivatives of $f\left(x\right)$, what must be true about $F\left(x\right)$ and $G\left(x\right)$?

If $f\left(x\right)$ and $g\left(x\right)$ are both antiderivatives of the same function, what must be true about $f\left(x\right)$ and $g\left(x\right)$?

Which of the following is an antiderivative of $f\left(x\right)=tan(e^x+2)$ on $0\le x\le ln\left(2\right)$?

Which of the following is the $5^{th}$-degree Maclaurin polynomial for the function $f\left(x\right)=e^{-x}$?