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Category: Integration

Question-148905

Question Number 148905 by DELETED last updated on 01/Aug/21 Answered by DELETED last updated on 01/Aug/21 $$\mathrm{Answered}: \\ $$$$−\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{5x}\:\right)\mathrm{dx}=−\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{5}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \right]\underset{\mathrm{2}} {\overset{\mathrm{4}}…

Question-83331

Question Number 83331 by oyemi kemewari last updated on 01/Mar/20 Commented by jagoll last updated on 01/Mar/20 $$\left(\mathrm{13}\right)\:\int\:\mathrm{sec}\:\mathrm{x}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{sec}\:\mathrm{x}\:\left(\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\right)\:\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}} \\ $$$$=\:\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{tan}\:\mathrm{x}} \\ $$$$=\:\int\:\frac{\mathrm{d}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}} \\ $$$$=\:\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\mid\:+\:\mathrm{c}…