Show Mobile Notice
Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 5.2 : Computing Indefinite Integrals
For problems 1 – 21 evaluate the given integral.
- \(\displaystyle \int{{4{x^6} - 2{x^3} + 7x - 4,円dx}}\) Solution
- \(\displaystyle \int{{{z^7} - 48{z^{11}} - 5{z^{16}},円dz}}\) Solution
- \(\displaystyle \int{{10{t^{ - 3}} + 12{t^{ - 9}} + 4{t^3},円dt}}\) Solution
- \(\displaystyle \int{{{w^{ - 2}} + 10{w^{ - 5}} - 8,円dw}}\) Solution
- \(\displaystyle \int{{12,円dy}}\) Solution
- \(\displaystyle \int{{\sqrt[3]{w} + 10,円,円\sqrt[5]{{{w^3}}},円dw}}\) Solution
- \(\displaystyle \int{{\sqrt {{x^7}} - 7,円\sqrt[6]{{{x^5}}} + 17,円,円\sqrt[3]{{{x^{10}}}},円dx}}\) Solution
- \(\displaystyle \int{{\frac{4}{{{x^2}}} + 2 - \frac{1}{{8{x^3}}},円dx}}\) Solution
- \(\displaystyle \int{{\frac{7}{{3{y^6}}} + \frac{1}{{{y^{10}}}} - \frac{2}{{\sqrt[3]{{{y^4}}}}},円dy}}\) Solution
- \(\displaystyle \int{{\left( {{t^2} - 1} \right)\left( {4 + 3t} \right),円dt}}\) Solution
- \(\displaystyle \int{{\sqrt z \left( {{z^2} - \frac{1}{{4z}}} \right),円dz}}\) Solution
- \(\displaystyle \int{{\frac{{{z^8} - 6{z^5} + 4{z^3} - 2}}{{{z^4}}},円dz}}\) Solution
- \(\displaystyle \int{{\frac{{{x^4} - \sqrt[3]{x}}}{{6\sqrt x }},円dx}}\) Solution
- \(\displaystyle \int{{\sin \left( x \right) + 10{{\csc }^2}\left( x \right),円dx}}\) Solution
- \(\displaystyle \int{{2\cos \left( w \right) - \sec \left( w \right)\tan \left( w \right),円dw}}\) Solution
- \(\displaystyle \int{{12 + \csc \left( \theta \right)\left[ {\sin \left( \theta \right) + \csc \left( \theta \right)} \right],円d\theta }}\) Solution
- \(\displaystyle \int{{4{{\bf{e}}^z} + 15 - \frac{1}{{6z}},円dz}}\) Solution
- \(\displaystyle \int{{{t^3} - \frac{{{{\bf{e}}^{ - t}} - 4}}{{{{\bf{e}}^{ - t}}}},円dt}}\) Solution
- \(\displaystyle \int{{\frac{6}{{{w^3}}} - \frac{2}{w},円dw}}\) Solution
- \(\displaystyle \int{{\frac{1}{{1 + {x^2}}} + \frac{{12}}{{\sqrt {1 - {x^2}} }},円dx}}\) Solution
- \(\displaystyle \int{{6\cos \left( z \right) + \frac{4}{{\sqrt {1 - {z^2}} }},円dz}}\) Solution
- Determine \(f\left( x \right)\) given that \(f'\left( x \right) = 12{x^2} - 4x\) and \(f\left( { - 3} \right) = 17\). Solution
- Determine \(g\left( z \right)\) given that \(g'\left( z \right) = 3{z^3} + \frac{7}{{2\sqrt z }} - {{\bf{e}}^z}\) and \(g\left( 1 \right) = 15 - {\bf{e}}\). Solution
- Determine \(h\left( t \right)\) given that \(h''\left( t \right) = 24{t^2} - 48t + 2\), \(h\left( 1 \right) = - 9\) and \(h\left( { - 2} \right) = - 4\). Solution
© 2003 - 2025 Paul Dawkins
Page Last Modified : 11/16/2022