Find the indefinite integral below. Do not include an arbitrary constant vector.

Name: Find the indefinite integral below. Do not include an arbitrary constant vector.
Brand: Quizplus
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Question

Find the indefinite integral below.  Do not include an arbitrary constant vector.

Quizplus · Accepted Answer

This question requires integration by substitution. Let u = x^2 + 1
Then, du/dx = 2x, so dx/2 = du/(2x)
Substituting u and dx in the integral, we get:
∫ (x^3 + x) e^(x^2 + 1) dx = ∫ ((x^2 + 1) * x) e^(x^2 + 1) dx = (1/2) ∫ e^u du
= (1/2) e^(x^2 + 1) + C
Thus, the correct answer is D.

Find the Indefinite Integral Below