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Popular >

integral of x^5Inx

Solution

\int x^{5} I n x d x

Solution

\frac{I n x ^{7}}{7} + C

Solution steps

\int x^{5} I n x d x

Take the constant out:

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

= I n \cdot \int x x^{5} d x

Simplify

x x^{5} : x^{6}

= I n \cdot \int x^{6} d x

Apply the Power Rule

: \frac{x ^{7}}{7}

= I n \frac{x ^{7}}{7}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{I n x ^{7}}{7}

Add a constant to the solution

= \frac{I n x ^{7}}{7} + C

Popular Examples

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\frac{d}{d x} (lo g_{10} (\frac{x}{x + 1}))

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x \to - 3 lim (f (x))

integral of sec^8(x)tan(x)

\int sec^{8} (x) tan (x) d x

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\frac{d}{d x} (- x + 2)

f(t)=cos(t)+t^2sin(t)

f (t) = cos (t) + t^{2} sin (t)

Frequently Asked Questions (FAQ)

What is the integral of x^5Inx ?
The integral of x^5Inx is (Inx^7)/7+C