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Section 5.1 : Indefinite Integrals

1. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{10{x^9} - 12{x^3} - 5\,dx}}\)
   2. \(\displaystyle \int{{10{x^9} - 12{x^3}\,dx - 5}}\)
2. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{{t^7} + 33{t^2} + 8t\,dt}}\)
   2. \(\displaystyle \int{{{t^7}\,dt}} + 33{t^2} + 8t\)
3. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{6{x^5} - 7{x^3} + 12{x^2} - 10\,dx}}\)
   2. \(\displaystyle \int{{6{x^5} - 7{x^3}\,dx}} + 12{x^2} - 10\)
   3. \(\displaystyle \int{{6{x^5}\,dx}} - 7{x^3} + 12{x^2} - 10\)
4. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{21{x^6} - 9{x^5} - {x^3} - x\,dx}}\)
   2. \(\displaystyle \int{{21{x^6} - 9{x^5} - {x^3}\,dx}} - x\)
   3. \(\displaystyle \int{{21{x^6} - 9{x^5}\,dx}} - {x^3} - x\)

For problems 5 – 9 evaluate the indefinite integral.

1. \(\displaystyle \int{{8{t^5} - 15{t^2} - 1\,dt}}\)
2. \(\displaystyle \int{{120{y^9} - 24{y^5} - 4{y^3}\,dy}}\)
3. \(\displaystyle \int{{dw}}\)
4. \(\displaystyle \int{{{x^9} + 14{x^6} - 10{x^3} + 13x\,dx}}\)
5. \(\displaystyle \int{{8{x^6} - {x^4} - 7{x^2} + 11x - 12\,dx}}\)
6. Determine \(f\left( x \right)\) given that \(f'\left( x \right) = 16{x^4} - 9{x^2} - x\).
7. Determine \(g\left( t \right)\) given that \(g'\left( t \right) = 4{t^5} + 16{t^2} - 18t + 72\).
8. Determine \(R\left( z \right)\) given that \(R'\left( z \right) = 4{z^{15}} + 121{z^{10}} + 20{z^5} + z - 4\).
9. Determine \(f\left( x \right)\) given that \(f''\left( x \right) = 8{x^3} - 12x + 3\).