alleryUsing integration by parts, $\displaystyle\int x e^x\,dx$ equals:
A$(x + 1) e^x + C$
B$\dfrac{x^2}{2} e^x + C$
C$(x - 1) e^x + C$
D$x e^x + C$
Answer & Solution
Correct answer: C. $(x - 1) e^x + C$
Take $u = x$ (algebraic) and $dv = e^x\,dx$, then $du = dx$ and $v = e^x$.
**By parts:** $\int x e^x\,dx = x e^x - \int e^x\,dx = x e^x - e^x + C = (x - 1) e^x + C$.
Keep practising Unit 6A: Indefinite Integrals & Fundamental Theorem
Browse all Unit 6A: Indefinite Integrals & Fundamental Theorem questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} The number of arbitrary constants in the general solution of a differential equation of orUsing the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:$\displaystyle\int \log x\,dx$ equals:$\displaystyle\int ec^2 x\,dx$ equals:$\displaystyle\int \dfrac{1}{ qrt{1 - x^2}}\,dx$ equals:$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals: