Explained: "Find indefinite integral. ∫e3x2+4xdx"

gonjenjemeb

Answered question

2021-11-20

Find indefinite integral.

\int e^{3 x^{2} + 4} x d x

Phisecome

Beginner2021-11-21Added 18 answers

Step 1
To find indefinite integral.

\int e^{3 x^{2} + 4} x d x

Step 2
Now,

\int e^{3 x^{2} + 4} x d x = \int e^{t} \times \frac{d t}{6}

[Let,

3 x^{2} + 4 = t, 6 x d x = d t

]

= \frac{e^{3 x^{2} + 4}}{6} + C

Alfonso Miller

Beginner2021-11-22Added 20 answers

Step 1: Use Integration by Substitution.
Let

u = 3 x^{2} + 4, d u = 6 x d x, t h e n x d x = \frac{1}{6} d u

Step 2: Using u and du above, rewrite

\int e^{3 x^{2} + 4} x d x

\int \frac{e^{u}}{6} d u

Step 3: Use Constant Factor Rule:

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

\frac{1}{6} \int e^{u} d u

Step 4: The integral of

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

\frac{e^{u}}{6}

Step 5: Substitute

u = 3 x^{2} + 4

back into the original integral.

\frac{e^{3 x^{2} + 4}}{6}

Step 6: Add constant.

\frac{e^{3 x^{2} + 4}}{6} + C

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