What is the integral of (5x-2)^7 ?

The integral of (5x-2)^7 is 1/40 (5x-2)^8+C

Popular >

integral of (5x-2)^7

\int (5 x - 2)^{7} d x

\frac{1}{40} (5 x - 2)^{8} + C

Solution steps

\int (5 x - 2)^{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 - 2

= \frac{1}{5} \cdot \frac{( 5 x - 2 ) ^{8}}{8}

Simplify

\frac{1}{5} \cdot \frac{( 5 x - 2 ) ^{8}}{8} : \frac{1}{40} (5 x - 2)^{8}

= \frac{1}{40} (5 x - 2)^{8}

Add a constant to the solution

= \frac{1}{40} (5 x - 2)^{8} + C

5 t

\frac{\partial}{\partial y} (\frac{y}{1 + x ^{2} y ^{2}})

\int_{π}^{2 π} x d x

\int \frac{- 1}{1 - ( 4 t + 1 ) ^{2}} d t

e^{x^{2} - 1}