What is the integral from 0 to 0.2 of (x^6)/(1+x^7) ?

The integral from 0 to 0.2 of (x^6)/(1+x^7) is 1.82856E-6

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integral from 0 to 0.2 of (x^6)/(1+x^7)

\int_{0}^{0.2} \frac{x ^{6}}{1 + x ^{7}} d x

1.82856 E - 6

Solution steps

\int_{0}^{0.2} \frac{x ^{6}}{1 + x ^{7}} d x

Apply u-substitution

= \int_{1}^{1.0000128} \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{1}^{1.0000128} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{7} [ln ∣ u ∣]_{1}^{1.0000128}

Simplify

= 0.14285 \dots [ln ∣ u ∣]_{1}^{1.0000128}

Compute the boundaries:

0.00001 \dots

= 0.14285 \dots \cdot 0.00001 \dots

Simplify

= 1.82856 E - 6

What is the integral from 0 to 0.2 of (x^6)/(1+x^7) ?
The integral from 0 to 0.2 of (x^6)/(1+x^7) is 1.82856E-6