The value of int e^{x}(x^{5}+5x^{4}+1)dx is | vedclass

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Question

(B) We know that $\int e^{x}(f(x)+f'(x))dx = e^{x}f(x)+c$. Here,let $f(x) = x^{5}$. Then,$f'(x) = 5x^{4}$. The given integral is $\int e^{x}(x^{5}+5x^

Vedclass · Accepted Answer

$e^{x}x^{5}+e^{x}+c$

Vedclass · Answer

(B) We know that $\int e^{x}(f(x)+f'(x))dx = e^{x}f(x)+c$. Here,let $f(x) = x^{5}$. Then,$f'(x) = 5x^{4}$. The given integral is $\int e^{x}(x^{5}+5x^{4}+1)dx$. We can rewrite this as $\int e^{x}(x^{5}+5x^{4})dx + \int e^{x}dx$. Using the formula $\int e^{x}(f(x)+f'(x))dx = e^{x}f(x)+c$,we get $\int e^{x}(x^{5}+5x^{4})dx = e^{x}x^{5}+c_1$. Thus,the total integral is $e^{x}x^{5} + e^{x} + c$.

The value of $\int e^{x}(x^{5}+5x^{4}+1)dx$ is

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