Category: Integration

Question Number 45670 by arvinddayama01@gmail.com last updated on 15/Oct/18 $$\int {cos}^{-1}\left(sinx\right)dx=?$$ Commented by maxmathsup by imad last updated on 15/Oct/18 $$letI=\int arccos\left(sinx\right)dxchangementarcos\left(sinx\right)=t\Rightarrow sinx=cost$$$$\Rightarrow{x}={arcsin}\left({cost}\right)\:\Rightarrow{dx}=−{sint}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{cos}^{\mathrm{2}}…

Question Number 111195 by bemath last updated on 02/Sep/20 $$\sqrt{\mathrm{bemath}}$$$$\int \frac{\mathrm{dx}}{\sqrt[3]{\mathrm{x}-1}\sqrt[3]{{(\mathrm{x}+1)}^2}}?$$ Answered by Sarah85 last updated on 02/Sep/20 $$\mathrm{substitute}\:{t}=\sqrt[{\mathrm{3}}]{\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}}\:\Leftrightarrow\:{x}=−\frac{{t}^{\mathrm{3}} +\mathrm{1}}{{t}^{\mathrm{3}} −\mathrm{1}}\:\Rightarrow…

Question Number 111174 by Her_Majesty last updated on 02/Sep/20 $$followingthenewesttrend-whatdoI$$$$say!?-aheadofit,ofcourse!Ipostthis$$$$answertooneofthenextquestions,look$$$$outforitsoyou{won}^{\prime }tmissit!$$$$$$$$I=I_1-2I_2=\xi \left(5\right)+\mathrm{\Gamma }\left(7/3\right)-2/\sqrt{\pi }+C$$ Terms…

Question Number 45632 by maxmathsup by imad last updated on 14/Oct/18 $$1)find\int ln(1+x^3)dx$$$$2)calculate{\int }_0^{1}ln(1+x^3)ex$$ Commented by maxmathsup by imad…

Question Number 176679 by mnjuly1970 last updated on 24/Sep/22 $$$$$$Eeasyintegral\dots .$$$$\:\:\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{−\int_{\mathrm{0}} ^{\:\infty} {e}^{\:−{x}^{\:\mathrm{2}} } {dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} {e}^{\:−{x}^{\:\mathrm{2}} } {dx}} {sin}^{\:\mathrm{2}} \left({t}\right).{ln}^{\:\mathrm{3}}…