If a > 0 then 1 a xp dx ò¥ converges if p >1 and. ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. Then a fxdx ò¥ divg. Web symbolab integrals cheat sheet common integrals: If a gxdx ò¥ divg. ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. Integrals of rational and irrational. If f(x) ‡‡gx( ) 0on [a,¥) then, 1. If a fxdx ò¥ conv.
Then a gxdx ò¥ conv. Then a gxdx ò¥ conv. If a fxdx ò¥ conv. If f(x) ‡‡gx( ) 0on [a,¥) then, 1. Integrals of rational and irrational. If a gxdx ò¥ divg. If a > 0 then 1 a xp dx ò¥ converges if p >1 and. ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). Then a fxdx ò¥ divg. Web comparison test for improper integrals : ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du.
