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When multiplying exponents with same base you can add the exponents: $ex^3x$
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$\int ex^{4}dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(x^3ex)dx. When multiplying exponents with same base you can add the exponents: ex^3x. The integral of a function times a constant (e) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 4. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.