3.5d Integration by Substitution Method | ∫18x²(6x³+5)^(1/4) dx | | ∫(1−1/w)cos(w−lnw) dw |

In this video, we solve the integral \int 18x^2(6x^3+5)^{1/4},dx using the **Substitution (u-Substitution) Method**. We show how to: Identify the inner function Choose the correct substitution (u=6x^3+5) Convert the integral into a simpler form Integrate using the power rule Find the final answer and verify the result This technique is essential for Calculus, Numerical Analysis, Engineering Mathematics, and Differential Equations. *Topics Covered:* Integration by Substitution u-Substitution Method Power Rule Integration Chain Rule in Reverse Calculus I #Calculus #Integration #USubstitution #Mathematics #EngineeringMath #IntegralCalculus #NumericalAnalysis #MathTutorial --- YouTube Title 2 *Integration by Substitution | ∫ 2/(t²+1)² dt | Easy u-Substitution Method* Description In this lecture, we solve the integral [ \int \frac{2t}{(t^2+1)^2},dt ] using the **u-Substitution Method**. Learn how to: Recognize composite functions Select an appropriate substitution Simplify complicated rational expressions Evaluate the integral step-by-step Check your answer by differentiation Perfect for students studying Calculus, Engineering Mathematics, and Applied Mathematics. *Topics Covered:* Integration by Substitution Rational Functions Calculus Techniques Indefinite Integrals Reverse Chain Rule #Integration #USubstitution #Calculus #EngineeringMathematics #MathLecture #IntegralCalculus #Mathematics --- YouTube Title 3 (Last One) *Integration by Substitution | ∫(1−1/w)cos(w−lnw) dw | Trigonometric Integral* Description In this video, we solve the challenging integral [ \int \left(1-\frac{1}{w}\right)\cos(w-\ln w),dw ] using the **Substitution Method (u-Substitution)**. You'll learn how to: Identify the inner expression (w-\ln w) Compute its derivative Apply u-substitution effectively Transform a complicated trigonometric integral into a simple one Obtain the final answer quickly and accurately This example demonstrates how recognizing a function and its derivative can make difficult integrals straightforward. *Topics Covered:* u-Substitution Method Trigonometric Integrals Chain Rule and Antiderivatives Integral Calculus Advanced Integration Techniques #Calculus #IntegrationBySubstitution #TrigonometricIntegrals #USubstitution #EngineeringMath #Mathematics #IntegralCalculus #MathTutorial