What is the integral of (2x-3)^5 ?

The integral of (2x-3)^5 is 1/12 (2x-3)^6+C

Popular >

integral of (2x-3)^5

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

\frac{1}{12} (2 x - 3)^{6} + C

Solution steps

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

Apply u-substitution

: \int \frac{u ^{5}}{2} d u

= \int \frac{u ^{5}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{5} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Substitute back

u = 2 x - 3

= \frac{1}{2} \cdot \frac{( 2 x - 3 ) ^{6}}{6}

Simplify

\frac{1}{2} \cdot \frac{( 2 x - 3 ) ^{6}}{6} : \frac{1}{12} (2 x - 3)^{6}

= \frac{1}{12} (2 x - 3)^{6}

Add a constant to the solution

= \frac{1}{12} (2 x - 3)^{6} + C

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

f (x) = x^{2}, at x = 5

\int 1 - cos (4 x) d x

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

\frac{5}{2 x ^{6}}