What is the integral from 0 to 1 of x^4(2+2x^5)^5 ?

The integral from 0 to 1 of x^4(2+2x^5)^5 is 336/5

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integral from 0 to 1 of x^4(2+2x^5)^5

\int_{0}^{1} x^{4} (2 + 2 x^{5})^{5} d x

\frac{336}{5}

Decimal

67.2

Solution steps

\int_{0}^{1} x^{4} (2 + 2 x^{5})^{5} d x

Apply u-substitution

= \int_{2}^{4} \frac{u ^{5}}{10} 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_{2}^{4} u^{5} d u

Apply the Power Rule

= \frac{1}{10} [\frac{u ^{6}}{6}]_{2}^{4}

Compute the boundaries:

672

= \frac{1}{10} \cdot 672

Simplify

= \frac{336}{5}

\int_{- 1}^{5} 5 + 4 x - x^{2} + 4 d x

\int_{0}^{a} (a^{2} x - x^{3}) d x

\int_{0}^{2} x^{3} - 4 x d x

\int_{- 3}^{6} ∣ x ∣ d x

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

What is the integral from 0 to 1 of x^4(2+2x^5)^5 ?
The integral from 0 to 1 of x^4(2+2x^5)^5 is 336/5