What is the integral of ((-1)^{n+1}(x-7)^n)/n ?

The integral of ((-1)^{n+1}(x-7)^n)/n is ((-1)^{n+1})/n*((x-7)^{n+1})/(n+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((-1)^{n+1}(x-7)^n)/n

\int \frac{( - 1 ) ^{n + 1} ( x - 7 ) ^{n}}{n} d x

\frac{( - 1 ) ^{n + 1}}{n} \cdot \frac{( x - 7 ) ^{n + 1}}{n + 1} + C

Solution steps

\int \frac{( - 1 ) ^{n + 1} ( x - 7 ) ^{n}}{n} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{( - 1 ) ^{n + 1}}{n} \cdot \int (x - 7)^{n} d x

Apply u-substitution

= \frac{( - 1 ) ^{n + 1}}{n} \cdot \int u^{n} d u

Apply the Power Rule

= \frac{( - 1 ) ^{n + 1}}{n} \cdot \frac{u ^{n + 1}}{n + 1}

Substitute back

u = x - 7

= \frac{( - 1 ) ^{n + 1}}{n} \cdot \frac{( x - 7 ) ^{n + 1}}{n + 1}

Add a constant to the solution

= \frac{( - 1 ) ^{n + 1}}{n} \cdot \frac{( x - 7 ) ^{n + 1}}{n + 1} + C

\int e^{- in t} d t

\int 9 x \cdot e^{3 x} d x

\int \frac{1}{x} e^{x^{2}} d x

\int \frac{3 x ^{2}}{2 ( 9 x ^{2} + 1 )} d x

\int \frac{e ^{2 t}}{t} d t

What is the integral of ((-1)^{n+1}(x-7)^n)/n ?
The integral of ((-1)^{n+1}(x-7)^n)/n is ((-1)^{n+1})/n*((x-7)^{n+1})/(n+1)+C