Integration by parts (IBP) Lecture Video
Evaluate the following integrals:
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\( \int \ln (x) \ \mathrm{d}x \qquad \quad \int x \ln (x) \ \mathrm{d}x \)
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\( \int x^7 \ln (x) \ \mathrm{d}x \) solution
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\( \int x\,e^{2x}\, \mathrm{d}x \qquad \quad \int x^2\,e^{2x}\, \mathrm{d}x \qquad \quad \int x^3\,e^{2x}\, \mathrm{d}x \) solution
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\( \int 5te^{-5t} \, \mathrm{d}t \) solution
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\( \int \ln (\sqrt{x}) \, \mathrm{d}x \) solution
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\( \int x \cos (x)\ \mathrm{d}x \) solution
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\( \int 5x \cos (3x)\ \mathrm{d}x \) solution
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\( \int x^2 \cos (2x)\ \mathrm{d}x \qquad \int x^3 \cos (2x)\ \mathrm{d}x \) solution
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\( \int x^2 \sin (x)\ \mathrm{d}x \) solution
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\( \int e^x \cos (x) \ \mathrm{d}x \) solution
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\( \int 6 \sin (3y) \, e^{2y} \ \mathrm{d}y \) solution
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\( \int \arcsin (x)\ \mathrm{d}x \) solution
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\(\int x^3\, e^{x^2}\, \mathrm{d}x\) solution
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\(\int \tan^{-1} (2x)\ \mathrm{d}x \) solution
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\(\displaystyle{\int_1^{\sqrt{3}} 8\arctan(1/x)\ \mathrm{d}x }\) solution
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\(\displaystyle{\int (\ln (x))^2 \mathrm{d}x }\) solution
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\(\displaystyle{\int_{0}^1 (x^2+1) \, e^x\ \mathrm{d}x}\) solution
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\(\int \sin \sqrt{x} \, \mathrm{d}x \) solution