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Popular >

integral of x^5In(x)

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

(d^2)/(dx^2)(8x^{-2})

\frac{d ^{2}}{d x ^{2}} (8 x^{- 2})

integral of (2x^2+x)*e^{-3x}

\int (2 x^{2} + x) \cdot e^{- 3 x} d x

derivative of-ln(2x-3)

\frac{d}{d x} (- ln (2 x - 3))

tangent of y=2x^3-x^2+4,(2,16)tangent of

y = 2 x^{3} - x^{2} + 4, (2, 16)

area x=(y^2-1)/3 ,x=3+y area

x = \frac{y ^{2} - 1}{3}, x = 3 + y

Frequently Asked Questions (FAQ)

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