How to integrate e raised to a fraction? Simpler than you think!
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Crack polynomial × exponential integrals fast using repeated integration by parts (tabular method). Let u = x^3 and dv = e^x dx. Differentiate u down to 0; integrate e^x each time. Alternate signs and multiply diagonally. Result: ∫ x^3 e^x dx = e^x(x^3 − 3x^2 6x − 6) C. Tip: For ∫ x^n e^x dx, the pattern ends after n 1 steps with coefficients from the factorial triangle. Hashtags: #Calculus #Integration #IntegrationByParts #TabularMethod #IndefiniteIntegral #MathReels #EngineeringMath #JEE #Stud
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Crack polynomial × exponential integrals fast using repeated integration by parts (tabular method). Let u = x^3 and dv = e^x dx. Differentiate u down to 0; integrate e^x each time. Alternate signs and multiply diagonally. Result: ∫ x^3 e^x dx = e^x(x^3 − 3x^2 6x − 6) C. Tip: For ∫ x^n e^x dx, the pattern ends after n 1 steps with coefficients from the factorial triangle. Hashtags: #Calculus #Integration #IntegrationByParts #TabularMethod #IndefiniteIntegral #MathReels #EngineeringMath #JEE #Stud
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Math Guy Steve on Instagram: "Integrate e^(sqrt(x)) dx — full solution (u-sub + IBP) u = sqrt(x), dx = 2u du ⇒ 2∫u e^u du. IBP gives 2(u e^u − e^u) + C. Back-sub: 2(sqrt(x) − 1)e^(sqrt(x)) + C. Save this, tag a classmate, and comment NEXT with the topic you want tomorrow. Follow for daily ACT/Calc help. #Calculus #Integration #USubstitution #IBP #MathHelp #STEM #Precalc #Algebra2 #StudyTok #MathGuySteve"
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