int e^{x} cdot x^{5} , dx is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We use the formula for integration by parts: $\int u \cdot v \, dx = u \int v \, dx - \int (u' \int v \, dx) \, dx$.Let $I = \int e^{x} \cdot x^{5

Vedclass · Accepted Answer

$e^{x}[x^{5}-5 x^{4}+20 x^{3}-60 x^{2}+120 x-120]+C$

Vedclass · Answer

(C) We use the formula for integration by parts: $\int u \cdot v \, dx = u \int v \, dx - \int (u' \int v \, dx) \, dx$.Let $I = \int e^{x} \cdot x^{5} \, dx$.Using the generalized integration by parts formula $\int e^{x} f(x) \, dx = e^{x} [f(x) - f'(x) + f''(x) - f'''(x) + f^{(4)}(x) - f^{(5)}(x)] + C$.Here,$f(x) = x^{5}$.Then,$f'(x) = 5x^{4}$,$f''(x) = 20x^{3}$,$f'''(x) = 60x^{2}$,$f^{(4)}(x) = 120x$,and $f^{(5)}(x) = 120$.Substituting these into the formula:$I = e^{x} [x^{5} - 5x^{4} + 20x^{3} - 60x^{2} + 120x - 120] + C$.

$\int e^{x} \cdot x^{5} \, dx$ is

Similar Questions

If $I_n = \int (\log x)^n \, dx$,then $I_n + n I_{n-1} =$

If $I(x) = \int x^2(\log x)^2 dx$ and $I(1) = 0$,then $I(x)$ is equal to:

If linear functions $f(x)$ and $g(x)$ satisfy $\int {\left[ {\left( {1 - 2x} \right)\cos x + \left( {3 + 2x} \right)\sin x} \right]} dx = f(x)\sin x + g(x)\cos x + C$ (where $C$ is the constant of integration),then which of the following is true?

The value of the integral $\int x^3 \cos x \, dx$ is:

$\int (x+1)^2 e^x \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module