## Review for Third part (section 007)

Note from the instructor: This is an amazing practice test! There are three really good questions, two of them specially challenging. I am missing at least one or two questions with definite integrals, and/or the use of the Fundamental Theorem of Calculus (this is part of the final exam!) I did change the coefficients of most of the problems to prevent the use of answer keys.

1. $\displaystyle{\int (x+2)e^{7x}\, dx}$
2. $\displaystyle{\int \frac{18x^2-4x}{6x^3-2x^2}\, dx}$
3. $\displaystyle{\int e^{3.7x}\, dx}$
4. $\displaystyle{\int \frac{3y}{\sqrt{17-y}}\, dx}$
5. $\displaystyle{\int x^{18}+16x-17\, dx}$
6. $\displaystyle{\int x^3(x^4+17)^{22}\, dx}$
7. $\displaystyle{\int \frac{dy}{y-9}\, dx}$
8. $\displaystyle{\int x^3 \sqrt{4x^5+3}\, dx}$
9. $\displaystyle{\int \frac{e^t+44}{e^t+44t}\, dt}$
10. $\displaystyle{\int x^5 \ln x\, dx}$
11. Find an antiderivative $F(x)$ of $f(x)=22e^x$ satisfying $F(0)=10.$
12. Find an antiderivative $F(x)$ of $f(x)=x^6-12x^4$ satisfying $F(0)=17.$