00:00Let's solve the sum that is integration of 3x square plus 2x plus 1 dx. Here f of x is equal to 3x square plus 2x plus 1. So applying integration that becomes integration of 3x square plus 2x plus 1 dx. By splitting integration on these of all of these terms that becomes integration of 3x square dx plus integration of 2x dx and plus integration of 1 dx.
00:22Here we use the power rule in the first two terms that becomes integration of x to the power n dx is equal to x to the power n plus 1 upon n plus 1 plus constant of integration. So the above equation will be by applying that power rule 3 times x to the power 2 plus 1 and same 2 plus 1 will be divided in the denominator. So that becomes 2 plus 1 plus next term will be 2 times x to the power 1 plus 1 and upon 1 plus 1. And the integration of constant number means 1 only 1 that becomes x. So plus x plus constant of integration.
00:52That is equal to 3 times x cube plus 3 plus 2 times x square upon 2 and plus x plus c. So that is equal to x cube plus x square plus x plus c min.
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