What is the integral from 0 to 3 of x/(1+5x^2) ?

The integral from 0 to 3 of x/(1+5x^2) is 1/10 ln(46)

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integral from 0 to 3 of x/(1+5x^2)

\int_{0}^{3} \frac{x}{1 + 5 x ^{2}} d x

\frac{1}{10} ln (46)

Solution steps

\int_{0}^{3} \frac{x}{1 + 5 x ^{2}} d x

Apply u-substitution

: \int_{1}^{46} \frac{1}{10 u} d u

= \int_{1}^{46} \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{1}^{46} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{1}^{46}

Compute the boundaries:

ln (46)

= \frac{1}{10} ln (46)

\int_{0}^{1} 1 x + 4 d x

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

\int_{2}^{5} (2 x - 3)^{4} d x

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

\int_{0}^{2} (6 x - 6) (8 x^{2} + 4) d x

What is the integral from 0 to 3 of x/(1+5x^2) ?
The integral from 0 to 3 of x/(1+5x^2) is 1/10 ln(46)