How do you evaluate the integral $\int e^{4 x} d x$ $inte^(4x) dx$ ?

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How do you evaluate the integral $\int e^{4 x} d x$ $inte^(4x) dx$ ?

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Answer 1 · 2014-08-13T18:33:12

We will use $u$ $u$ -substitution, letting $u = 4 x$ $u = 4x$ .

Thus, $d u = 4 d x$ $du = 4dx$ .

Also, we will use the constant law of integration, namely $\int C \cdot f (x) d x = C \cdot \int f (x) d x$ $int C*f(x)dx = C*int f(x) dx$ to rewrite the integral so that it contains $d u$ $du$ :

$\int e^{4 x} d x = \frac{1}{4} \int 4 \cdot e^{4 x} d x$ $int e^(4x)dx = 1/4 int 4*e^(4x)dx$

Now, we will rewrite in terms of $u$ $u$ :

$\int e^{4 x} d x = \frac{1}{4} \int e^{u} d u$ $int e^(4x)dx = 1/4 int e^(u)du$

We know that the integral of $e^{u} d u$ $e^u du$ will simply be $e^{u}$ $e^u$ . Remember the constant of integration:

$\int e^{4 x} d x = \frac{1}{4} e^{u} + C$ $int e^(4x)dx = 1/4 e^(u) + C$

Substituting back $u$ $u$ gives:

$\int e^{4 x} d x = \frac{1}{4} e^{4 x} + C$ $int e^(4x)dx = 1/4 e^(4x) + C$

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How do you evaluate the integral $\int e^{4 x} d x$ $inte^(4x) dx$ ?

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