Use the Exponential Rule to find the indefinite integral. \int 7xe^{0.5x^{2}}dx

Clifland

Clifland

Answered question

2021-11-10

Use the Exponential Rule to find the indefinite integral.
7xe0.5x2dx

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2021-11-11Added 98 answers

Step 1
The integral is
7xe0.5x2dx
Step 2
Consider the substitution
u=0.5x2, then differentiation becomes du=xdx
Step 3
Change the integral and compute as follows.
7xe0.5x2dx=7eudu (as u=0.5x2,du=xdx)
=7eu+C (exdx)
=7e0.5x2+C (Substitute back u)
Step 4
Therefore,
7xe0.5x2dx=7e0.5x2+C

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