What is the integral from 1 to 3 of x/((3x^2-1)^3) ?

The integral from 1 to 3 of x/((3x^2-1)^3) is 7/338

Popular >

integral from 1 to 3 of x/((3x^2-1)^3)

\int_{1}^{3} \frac{x}{( 3 x ^{2} - 1 ) ^{3}} d x

\frac{7}{338}

Decimal

0.02071 \dots

Solution steps

\int_{1}^{3} \frac{x}{( 3 x ^{2} - 1 ) ^{3}} d x

Apply u-substitution

: \int_{2}^{26} \frac{1}{6 u ^{3}} d u

= \int_{2}^{26} \frac{1}{6 u ^{3}} 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_{2}^{26} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{2}^{26}

= \frac{1}{6} [- \frac{1}{2 u ^{2}}]_{2}^{26}

Compute the boundaries:

\frac{21}{169}

= \frac{1}{6} \cdot \frac{21}{169}

Simplify

= \frac{7}{338}

\int_{0}^{\frac{π}{6}} e^{i 2 t} d t

\int_{0}^{4} ln (t) d t

\int_{0}^{π} 1 - cos (2 x) d x

\int_{2}^{3} \frac{1}{x - x} d x

\int_{0}^{2} 1 - x^{2} d x

What is the integral from 1 to 3 of x/((3x^2-1)^3) ?
The integral from 1 to 3 of x/((3x^2-1)^3) is 7/338