What is the integral of (1-x)^5 ?

The integral of (1-x)^5 is -((1-x)^6)/6+C

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integral of (1-x)^5

\int (1 - x)^{5} d x

- \frac{( 1 - x ) ^{6}}{6} + C

Solution steps

\int (1 - x)^{5} d x

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= - \frac{u ^{6}}{6}

Substitute back

u = 1 - x

= - \frac{( 1 - x ) ^{6}}{6}

Add a constant to the solution

= - \frac{( 1 - x ) ^{6}}{6} + C

n = 1 \sum \infty 8 \cdot (\frac{1}{3})^{n}

\frac{d}{d x} (\frac{( x ^{2} - 5 x ) ^{2}}{( 6 x + 7 ) ^{3}})

(- 5, 5), (- 7, 5)

\frac{d}{d x} (\frac{5 x ^{2} - 15}{3 ( x ^{2} - 5 ) ^{\frac{2}{3}}})

x \to a lim (0^{0})