What is the integral of (4x-5)^6 ?

The integral of (4x-5)^6 is 1/28 (4x-5)^7+C

Popular >

integral of (4x-5)^6

\int (4 x - 5)^{6} d x

\frac{1}{28} (4 x - 5)^{7} + C

Solution steps

\int (4 x - 5)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{4} d u

= \int \frac{u ^{6}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{1}{4} \cdot \frac{u ^{7}}{7}

Substitute back

u = 4 x - 5

= \frac{1}{4} \cdot \frac{( 4 x - 5 ) ^{7}}{7}

Simplify

\frac{1}{4} \cdot \frac{( 4 x - 5 ) ^{7}}{7} : \frac{1}{28} (4 x - 5)^{7}

= \frac{1}{28} (4 x - 5)^{7}

Add a constant to the solution

= \frac{1}{28} (4 x - 5)^{7} + C

\int \frac{1}{( 1 + e ^{x} )} d x

\int x^{2} + 2 x - 35 d x

\int 2 x + 4 cos (x) d x

\int 2 x - sec^{2} (x) d x

\int 27 sin^{3} (x) d x