Best solutions to - "Use the Exponential Rule to find the indefinite..."

Clifland

Answered question

2021-11-10

Use the Exponential Rule to find the indefinite integral.

\int 7 x e^{0.5 x^{2}} d x

Leonard Stokes

Skilled2021-11-11Added 98 answers

Step 1
The integral is

\int 7 x e^{0.5 x^{2}} d x

Step 2
Consider the substitution

u = 0.5 x^{2}

, then differentiation becomes du=xdx
Step 3
Change the integral and compute as follows.

\int 7 x e^{0.5 x^{2}} d x = 7 \int e^{u} d u

(as

u = 0.5 x^{2}, d u = x d x

)

= 7 e^{u} + C

(

∵ \int e^{x} d x

)

= 7 e^{0.5 x^{2}} + C

(Substitute back u)
Step 4
Therefore,

\int 7 x e^{0.5 x^{2}} d x = 7 e^{0.5 x^{2}} + C

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