Calculate or simplify the expression .
Evaluate the integral by following steps:
step0: Evaluate using partial integration formula:
step1: Prepare for integration by parts:
step2: Calculate the derivative:
step3: Evaluate the integral:
step4: Substitute the values into formula:
step5: Calculate:
step6: Evaluate the integral:
step7: Simplify the expression:
step8: Simplify the expression:
step9: Add the constant of integral C:
La integral de con respecto a es igual a , donde es una constante real.
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The Deep Dive
To solve the integral , you can use integration by parts. Set and . Then, differentiate and integrate accordingly: and . After applying integration by parts, you will arrive at a formula involving another integral that can be recursively solved.
By repeatedly applying integration by parts, you’ll finally simplify the terms and arrive at the solution for the integral. Don’t forget to add the constant of integration at the end!