What is the integral from b to 2b of x^5 ?

The integral from b to 2b of x^5 is (21b^6)/2

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integral from b to 2b of x^5

\int_{b}^{2 b} x^{5} d x

\frac{21 b ^{6}}{2}

Solution steps

\int_{b}^{2 b} x^{5} d x

Apply the Power Rule

: [\frac{x ^{6}}{6}]_{b}^{2 b}

= [\frac{x ^{6}}{6}]_{b}^{2 b}

Compute the boundaries:

\frac{32 b ^{6}}{3} - \frac{b ^{6}}{6}

= \frac{32 b ^{6}}{3} - \frac{b ^{6}}{6}

Simplify

= \frac{21 b ^{6}}{2}

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

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

x^{2} y^{^{''}} - 7 x y^{^{'}} + 16 y = 0

y = - 3 x^{3} + x^{2} + 10 x, x \geq 0

y^{^{''}} - 2 y^{^{'}} - 3 y = x e^{x}

What is the integral from b to 2b of x^5 ?
The integral from b to 2b of x^5 is (21b^6)/2