What is the integral of y(y^2+5)^8 ?

The integral of y(y^2+5)^8 is 1/18 (y^2+5)^9+C

Popular >

integral of y(y^2+5)^8

\int y (y^{2} + 5)^{8} d y

\frac{1}{18} (y^{2} + 5)^{9} + C

Solution steps

\int y (y^{2} + 5)^{8} d y

Apply u-substitution

: \int \frac{u ^{8}}{2} d u

= \int \frac{u ^{8}}{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^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{1}{2} \cdot \frac{u ^{9}}{9}

Substitute back

u = y^{2} + 5

= \frac{1}{2} \cdot \frac{( y ^{2} + 5 ) ^{9}}{9}

Simplify

\frac{1}{2} \cdot \frac{( y ^{2} + 5 ) ^{9}}{9} : \frac{1}{18} (y^{2} + 5)^{9}

= \frac{1}{18} (y^{2} + 5)^{9}

Add a constant to the solution

= \frac{1}{18} (y^{2} + 5)^{9} + C

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

\int 324 - x^{2} d x

\int \frac{x ^{2} + 2 x - 3}{x ^{3} - 2 x ^{2} + x - 2} d x

\int - \frac{e ^{x}}{( e ^{x} + 1 ) ^{3}} d x

\int u^{1.1} (\frac{1}{3 u} - 1) d u

What is the integral of y(y^2+5)^8 ?
The integral of y(y^2+5)^8 is 1/18 (y^2+5)^9+C