What is the integral of x(x^2+1)^6 ?

The integral of x(x^2+1)^6 is 1/14 (x^2+1)^7+C

Popular >

integral of x(x^2+1)^6

\int x (x^{2} + 1)^{6} d x

\frac{1}{14} (x^{2} + 1)^{7} + C

Solution steps

\int x (x^{2} + 1)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{2} d u

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{7}}{7}

Substitute back

u = x^{2} + 1

= \frac{1}{2} \cdot \frac{( x ^{2} + 1 ) ^{7}}{7}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 1 ) ^{7}}{7} : \frac{1}{14} (x^{2} + 1)^{7}

= \frac{1}{14} (x^{2} + 1)^{7}

Add a constant to the solution

= \frac{1}{14} (x^{2} + 1)^{7} + C

\frac{\partial}{\partial x} (\frac{86}{2 + x ^{2} + y ^{2}})

\frac{d}{d x} ((2 x - 2)^{4} (x^{2} + x + 1)^{5})

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

\int_{1}^{3} 4 x e^{x} d x

x \to 1 lim (π)

What is the integral of x(x^2+1)^6 ?
The integral of x(x^2+1)^6 is 1/14 (x^2+1)^7+C