What is the integral of x(3x^2-5)^{10} ?

The integral of x(3x^2-5)^{10} is 1/66 (3x^2-5)^{11}+C

integral of x(3x^2-5)^{10}

\int x (3 x^{2} - 5)^{10} d x

\frac{1}{66} (3 x^{2} - 5)^{11} + C

Solution steps

\int x (3 x^{2} - 5)^{10} d x

Apply u-substitution

= \int \frac{u ^{10}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u^{10} d u

Apply the Power Rule

= \frac{1}{6} \cdot \frac{u ^{11}}{11}

Substitute back

u = 3 x^{2} - 5

= \frac{1}{6} \cdot \frac{( 3 x ^{2} - 5 ) ^{11}}{11}

Simplify

\frac{1}{6} \cdot \frac{( 3 x ^{2} - 5 ) ^{11}}{11} : \frac{1}{66} (3 x^{2} - 5)^{11}

= \frac{1}{66} (3 x^{2} - 5)^{11}

Add a constant to the solution

= \frac{1}{66} (3 x^{2} - 5)^{11} + C

\int x^{4} e^{5 x} d x

f (x) = \frac{3}{x + 5}

d er i v a t i v e y = \frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}}

\frac{\partial}{\partial x} (x \cdot sin (4 \cdot y \cdot z^{4}))

t an g e n t f (x) = 2 x^{2} - 4 x, at x = - 1

What is the integral of x(3x^2-5)^{10} ?
The integral of x(3x^2-5)^{10} is 1/66 (3x^2-5)^{11}+C