What is the integral of e^x-e^a(x-a) ?

The integral of e^x-e^a(x-a) is e^x-e^a((x^2)/2-ax)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^x-e^a(x-a)

\int e^{x} - e^{a} (x - a) d x

e^{x} - e^{a} (\frac{x ^{2}}{2} - a x) + C

Solution steps

\int e^{x} - e^{a} (x - a) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x} d x - \int e^{a} (x - a) d x

\int e^{x} d x = e^{x}

\int e^{a} (x - a) d x = e^{a} (\frac{x ^{2}}{2} - a x)

= e^{x} - e^{a} (\frac{x ^{2}}{2} - a x)

Add a constant to the solution

= e^{x} - e^{a} (\frac{x ^{2}}{2} - a x) + C

\int \frac{3 x ^{3} + 8 x}{( x ^{2} + 2 ) ^{2}} d x

\frac{\partial}{\partial x} (p (q, x) q)

\frac{d}{d x} (x (2 x + 3)^{4})

\int \frac{1}{x} x^{'} d x

\frac{d}{d x} (sin (\frac{x}{1 + y}))

What is the integral of e^x-e^a(x-a) ?
The integral of e^x-e^a(x-a) is e^x-e^a((x^2)/2-ax)+C