Integrals Rules Sheet - Then a fxdx Γ²Β₯ divg. β« f ( g ( x )) g β² ( x ) dx = β« f ( u ) du. If a > 0 then 1 a xp dx Γ²Β₯ converges if p >1 and. Web symbolab integrals cheat sheet common integrals: Web comparison test for improper integrals : β« f ( x ) g β² ( x ) dx = f ( x ) g ( x ) β β« g ( x ) f β² ( x ) dx. If f(x) β‘β‘gx( ) 0on [a,Β₯) then, 1. If a fxdx Γ²Β₯ conv. If a gxdx Γ²Β₯ divg. β«π₯β1 π₯=ln(π₯) β« π₯ π₯ =ln(π₯) β« |π₯ π₯=π₯βπ₯ 2 2 β« π₯ π₯= π₯ β«sin(π₯) π₯=βcos(π₯) β«cos(π₯) π₯=sin(π₯).
Then a gxdx Γ²Β₯ conv. If a gxdx Γ²Β₯ divg. β«π₯β1 π₯=ln(π₯) β« π₯ π₯ =ln(π₯) β« |π₯ π₯=π₯βπ₯ 2 2 β« π₯ π₯= π₯ β«sin(π₯) π₯=βcos(π₯) β«cos(π₯) π₯=sin(π₯). Web comparison test for improper integrals : Web symbolab integrals cheat sheet common integrals: β« f ( x ) g β² ( x ) dx = f ( x ) g ( x ) β β« g ( x ) f β² ( x ) dx. If a fxdx Γ²Β₯ conv. If f(x) β‘β‘gx( ) 0on [a,Β₯) then, 1. Integrals of rational and irrational. β« f ( g ( x )) g β² ( x ) dx = β« f ( u ) du. Then a fxdx Γ²Β₯ divg. If a > 0 then 1 a xp dx Γ²Β₯ converges if p >1 and.