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Practice Problems for 5/1

  1. Evaluate the following indefinite integrals.
    1. \(\int \frac{\sec^2(x)}{(5-\tan x)^7}\, dx \)

    2. \(\int 9xe^{5-3x^2}\, dx\)


  2. Evaluate the following definite integrals.
    1. \(\int_{-1}^3 (2+6x^2)(x+x^3)^{3/4} \, dx \)

    2. \(\int_0^{\ln(\pi-2)} e^x\cos(2+e^x)\, dx\)


  3. Find the average value of \(f(x)=x(5+x^2)^2\) on the interval \([0,5]\).