How do you use substitution to integrate $6 x e^{4 x^{2}} d x$ $6 x e^{4 x^2} dx$ ?

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How do you use substitution to integrate $6 x e^{4 x^{2}} d x$ $6 x e^{4 x^2} dx$ ?

1 Answer

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Answer 1 · 2015-09-13T21:18:32

$\frac{3}{4} e^{4 x^{2}} + C$ $3/4e^(4x^2)+C$

Explanation:

Let $t = 4 x^{2}$ $t=4x^2$ , then $d t = 8 x d x \Rightarrow x d x = \frac{d t}{8}$ $dt=8xdx => xdx=dt/8$ . So,
$\int 6 x e^{4 x^{2}} d x = \int 6 \frac{d t}{8} e^{t} = \frac{3}{4} \int e^{t} d t = \frac{3}{4} e^{t} + C = \frac{3}{4} e^{4 x^{2}} + C$ $int6xe^(4x^2)dx=int6dt/8 e^t=3/4inte^tdt=3/4e^t+C=3/4e^(4x^2)+C$

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How do you use substitution to integrate $6 x e^{4 x^{2}} d x$ $6 x e^{4 x^2} dx$ ?

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How do you use substitution to integrate 6xe4x2dx6 x e^{4 x^2} dx?

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How do you use substitution to integrate $6 x e^{4 x^{2}} d x$ $6 x e^{4 x^2} dx$ ?