7. Antiderivatives & Indefinite Integrals

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 $f\left(x\right)=e^{-x}$?

Suppose $F\left(x\right)$ is an antiderivative of $f\left(x\right)$. Which of the following statements about the indefinite integral $\int f\left(x\right) dx$ is true?

Let $h\left(x\right)$ be an antiderivative of the function $f\left(x\right)=x^3+\frac{-\sin x}{x^2}+2$. Which of the following is a correct expression for $h\left(x\right)$?

Suppose the graph of a function $f$ is shown below. Which of the following graphs could represent an antiderivative $F$ of $f$?

Find the antiderivative of the following function.

$f\left(x\right)=5x^4$

Find the antiderivative of the following function.

$f\left(x\right)=10x^9$