Step-by-step Solution

Find the integral $\int3e^x\cdot xdx$

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Step-by-step Solution

Problem to solve:

$\int3\cdot e^x\cdot xdx$

Solving method

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

$3\int e^x\cdot xdx$

Unlock this full step-by-step solution!

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(3*2.718281828459045^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^x\cdot 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^x 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.

Final Answer

$3e^x\cdot x-3e^x+C_0$