009B Sample Final 1, Problem 4

Compute the following integrals.

a) $\int e^{x}(x+\sin(e^{x}))~dx$

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \frac{2x^2+1}{2x^2+x}~dx}

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \sin^3x~dx}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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