Get the solution to "Evaluate the integral of xex2dx"

kiki195ms

Answered question

2021-11-19

Evaluate the integral of

x e^{x^{2}} d x

Camem1937

Beginner2021-11-20Added 10 answers

Step 1
To determine the value of the integral.
Step 2
Given:

I = \int x e^{x^{2}} d x

Step 3
Let

u = x^{2}

, du=2xdx.

I = \int x e^{x^{2}} d x

I = \int e^{u} \frac{1}{2} d u

I = \frac{1}{2} \int e^{u} d u

I = \frac{1}{2} (e^{u}) + C

I = \frac{e^{x^{2}}}{2} + C

Step 4
Thus, the value of the integral is.

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

Marian Tucker

Beginner2021-11-21Added 15 answers

Step 1
Use Integration by Substitution.
Let

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

, then

x d x = \frac{1}{2} d u

Step 2
Using u and du above, rewrite

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

\int \frac{e^{u}}{2} d u

Step 3
Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

\frac{1}{2} \int e^{u} d u

Step 4
The integral of

e^{x} i s e^{x}

\frac{e^{u}}{2}

Step 5
Substitute

u = x^{2}

back into the original integral.

\frac{e^{x^{2}}}{2}

Step 6
Add constant.

\frac{e^{x^{2}}}{2} + C

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