Pregunta
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The integral of
with respect to
is
.
Solución
Calculate the integral
.
Evaluate the integral by following steps:
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: Add the constant of integral C:
The integral of with respect to is , where is an arbitrary constant.
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Como
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The Deep Dive
To solve the integral
, we can use integration by parts. Let
and
. Then,
and
. Now, applying integration by parts yields:
Calculating the remaining integral, we have:
Combining everything, we get:

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