What is the integral from 0 to 3 of x/(1+10x^2) ?

The integral from 0 to 3 of x/(1+10x^2) is 1/20 ln(91)

Popular >

integral from 0 to 3 of x/(1+10x^2)

\int_{0}^{3} \frac{x}{1 + 10 x ^{2}} d x

\frac{1}{20} ln (91)

Decimal

0.22554 \dots

Solution steps

\int_{0}^{3} \frac{x}{1 + 10 x ^{2}} d x

Apply u-substitution

: \int_{1}^{91} \frac{1}{20 u} d u

= \int_{1}^{91} \frac{1}{20 u} d u

Take the constant out:

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

= \frac{1}{20} \cdot \int_{1}^{91} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{20} [ln ∣ u ∣]_{1}^{91}

Compute the boundaries:

ln (91)

= \frac{1}{20} ln (91)

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

\int_{0}^{1} sec^{2} (x) d x

\int_{125}^{216} 3 y d y

\int_{2}^{3} x^{3} - 5 x^{2} + 6 x d x

\int_{0}^{2 π} 16 sin^{2} (t) d t

What is the integral from 0 to 3 of x/(1+10x^2) ?
The integral from 0 to 3 of x/(1+10x^2) is 1/20 ln(91)