What is the integral from 0 to 1 of x(4\sqrt[3]{x}+7\sqrt[4]{x}) ?

The integral from 0 to 1 of x(4\sqrt[3]{x}+7\sqrt[4]{x}) is 304/63

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integral from 0 to 1 of x(4\sqrt[3]{x}+7\sqrt[4]{x})

\frac{304}{63}

Decimal Notation

4.82539 \dots

Solution steps

Expand

= \int_{0}^{1} 4 x^{\frac{4}{3}} + 7 x^{\frac{5}{4}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} 4 x^{\frac{4}{3}} d x + \int_{0}^{1} 7 x^{\frac{5}{4}} d x

\int_{0}^{1} 4 x^{\frac{4}{3}} d x = \frac{12}{7}

\int_{0}^{1} 7 x^{\frac{5}{4}} d x = \frac{28}{9}

= \frac{12}{7} + \frac{28}{9}

Simplify

\frac{12}{7} + \frac{28}{9} : \frac{304}{63}

= \frac{304}{63}

y = e^{2 e^{x}}

x \to 3 lim (x^{2} - x - 6)

\int_{1}^{8} 7 \frac{ln ( x )}{x ^{2}} d x

\frac{s - 2}{s ^{2} - 7 s + 6}

x^{- 6} + e^{2 x}

What is the integral from 0 to 1 of x(4\sqrt[3]{x}+7\sqrt[4]{x}) ?
The integral from 0 to 1 of x(4\sqrt[3]{x}+7\sqrt[4]{x}) is 304/63