In Exercises 1–3, use integration by parts to find the indefinite integral.
To calculate: The infinite integral of
Given Information:
The integral is
Formula used:
The integration by part of two differentiable function is,
The basic rule of integration for constant C is,
The simple power rule of integration is,
Where,
The chain rule of differentiation is,
Calculation:
Consider the provided integral,
Since, the integrand of the provided indefinite integral is
Let the first function is
Differentiate both side with respect to x, use the simple power rule of differentiation.
Let the second function
Integrate both side with respect to x, use the integration for exponential.
Now, use the integration by parts method
Substitute
Further solve the integration by parts,
Consider, the integrand
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