What is the integral of (5x-1)^7 ?

The integral of (5x-1)^7 is 1/40 (5x-1)^8+C

Popular >

integral of (5x-1)^7

\int (5 x - 1)^{7} d x

\frac{1}{40} (5 x - 1)^{8} + C

Solution steps

\int (5 x - 1)^{7} d x

Apply u-substitution

: \int \frac{u ^{7}}{5} d u

= \int \frac{u ^{7}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{1}{5} \cdot \frac{u ^{8}}{8}

Substitute back

u = 5 x - 1

= \frac{1}{5} \cdot \frac{( 5 x - 1 ) ^{8}}{8}

Simplify

\frac{1}{5} \cdot \frac{( 5 x - 1 ) ^{8}}{8} : \frac{1}{40} (5 x - 1)^{8}

= \frac{1}{40} (5 x - 1)^{8}

Add a constant to the solution

= \frac{1}{40} (5 x - 1)^{8} + C

2 x, 9 x - x^{2}, (7, 14)

f (x) = \frac{6}{ln ( x ^{2} + 4 )}

\int \frac{sin ( 44 x )}{1 + cos ^{2} ( 44 x )} d x

\int 2 x (x^{2} + 1)^{- 7} d x

f (x) = x^{2}, [0, 3]