1. Evaluate the integral

∫x5(x^6−10)^47dx

by making the substitution u=x^6−10.

=_+C

2. Evaluate the indefinite integral.

∫7dx/xln(8x)

=_ + C

3. Evaluate the indefinite integral.

∫x^8e^x^9dx

=_+C

4. Evaluate the indefinite integral.

∫x4(15+x^5)^1/2dx

=_+C

5. Evaluate the indefinite integral.

∫4/(t+5)^8 dt

=_+C

6. Evaluate the indefinite integral:

∫x/x^2+4 dx

=_+C

7. A cell culture contains 4 thousand cells, and is growing at a rate of r(t)=11e^0.24t thousand cells per hour.

Find the total cell count after 4 hours. Give your answer accurate to at least 2 decimal places.

_ thousand cells

8. Use integration by parts to evaluate the integral:

∫2te^tdt =

9. ∫4xe^7xdx = + C

10. Use integration by parts to evaluate the integral:

∫ln(7x−1)dx

11. Use integration by parts to evaluate the integral:

∫ln(z)√z^13dz

12. Find ∫4x/3x+2dx

=_+C

13. Integrate: ∫x/(x^4+25)^1/2dx

=_ + C

14. Find ∫(−2x^2+3/x−1/x^4+4√x)dx

=_ + C

15. Find ∫(x+4)(x−6)dx

=_ + C

16. The traffic flow rate (cars per hour) across an intersection is r(t)=400+700t−270t2r(t)=400+700t-270t^2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 7 am?

_cars

17. A company’s marginal cost function is 17/√x where *x* is the number of units.

Find the total cost of the first 36 units (of increasing production from *x*=0 to *x*=36)

Total cost: $

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