Step-by-step Solution

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Step-by-step explanation

Problem to solve:

$\int7\cdot e^{8x}\cdot xdx$

Learn how to solve integrals of exponential functions problems step by step online.

$7\int e^{8x}xdx$

Learn how to solve integrals of exponential functions problems step by step online. Compute the integral int(7*2.718281828459045^(8*x)*x)dx. The integral of a constant by a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int e^{8x}xdx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that e^{8x} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

$\frac{7}{8}e^{8x}x-\frac{7}{64}e^{8x}+C_0$
$\int7\cdot e^{8x}\cdot xdx$