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Question Number 129788 by bramlexs22 last updated on 19/Jan/21

 ∫ (1+3x^3 )e^x^3   dx

$$\:\int\:\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right){e}^{{x}^{\mathrm{3}} } \:{dx}\: \\ $$

Answered by EDWIN88 last updated on 19/Jan/21

 let z = xe^x^3   ⇒ dz = (e^x^3  +x.(3x^2 e^x^3  ))dx   dz = (1+3x^3 )e^x^3   dx  I=∫ dz = z + c = xe^x^3   + C

$$\:\mathrm{let}\:\mathrm{z}\:=\:{xe}^{{x}^{\mathrm{3}} } \:\Rightarrow\:{dz}\:=\:\left({e}^{{x}^{\mathrm{3}} } +{x}.\left(\mathrm{3}{x}^{\mathrm{2}} {e}^{{x}^{\mathrm{3}} } \right)\right){dx} \\ $$$$\:{dz}\:=\:\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right){e}^{{x}^{\mathrm{3}} } \:{dx} \\ $$$${I}=\int\:{dz}\:=\:{z}\:+\:{c}\:=\:{xe}^{{x}^{\mathrm{3}} } \:+\:\mathrm{C}\: \\ $$

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