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Section 7.1 : Integration by Parts

Evaluate each of the following integrals.

1. \( \displaystyle \int{{4x\cos \left( {2 - 3x} \right)\,dx}}\) Solution
2. \( \displaystyle \int_{6}^{0}{{\left( {2 + 5x} \right){{\bf{e}}^{\frac{1}{3}x}}\,dx}}\) Solution
3. \( \displaystyle \int{{\left( {3t + {t^2}} \right)\sin \left( {2t} \right)\,dt}}\) Solution
4. \( \displaystyle \int{{6{{\tan }^{ - 1}}\left( {\frac{8}{w}} \right)\,dw}}\) Solution
5. \( \displaystyle \int{{{{\bf{e}}^{2z}}\cos \left( {\frac{1}{4}z} \right)\,dz}}\) Solution
6. \( \displaystyle \int_{0}^{\pi }{{{x^2}\cos \left( {4x} \right)\,dx}}\) Solution
7. \( \displaystyle \int{{{t^7}\sin \left( {2{t^4}} \right)\,dt}}\) Solution
8. \( \displaystyle \int{{{y^6}\cos \left( {3y} \right)\,dy}}\) Solution
9. \( \displaystyle \int{{\left( {4{x^3} - 9{x^2} + 7x + 3} \right){{\bf{e}}^{ - x}}\,dx}}\) Solution