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Section 5.1 : Indefinite Integrals

1. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{6{x^5} - 18{x^2} + 7\,dx}}\)
   2. \(\displaystyle \int{{6{x^5}\,dx}} - 18{x^2} + 7\)
   Solution
2. Evaluate each of the following indefinite integrals.
   1. \(\displaystyle \int{{40{x^3} + 12{x^2} - 9x + 14\,dx}}\)
   2. \(\displaystyle \int{{40{x^3} + 12{x^2} - 9x\,dx}} + 14\)
   3. \(\displaystyle \int{{40{x^3} + 12{x^2}\,dx}} - 9x + 14\)
   Solution

For problems 3 – 5 evaluate the indefinite integral.

1. \(\displaystyle \int{{12{t^7} - {t^2} - t + 3\,dt}}\) Solution
2. \(\displaystyle \int{{10{w^4} + 9{w^3} + 7w\,\,dw}}\) Solution
3. \(\displaystyle \int{{{z^6} + 4{z^4} - {z^2}\,dz}}\) Solution
4. Determine \(f\left( x \right)\) given that \(f'\left( x \right) = 6{x^8} - 20{x^4} + {x^2} + 9\). Solution
5. Determine \(h\left( t \right)\) given that \(h'\left( t \right) = {t^4} - {t^3} + {t^2} + t - 1\). Solution