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Popular >

integral of x^5inx

Solution

\int x^{5} in x d x

Solution

\frac{in x ^{7}}{7} + C

Solution steps

\int x^{5} in x d x

Take the constant out:

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

= in \cdot \int x^{5} x d x

Simplify

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

= in \cdot \int x^{6} d x

Apply the Power Rule

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

= in \frac{x ^{7}}{7}

Multiply fractions:

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

= \frac{in x ^{7}}{7}

Add a constant to the solution

= \frac{in x ^{7}}{7} + C

Graph

Popular Examples

integral of (12x)/(sqrt(1+4))

\int \frac{12 x}{1 + 4} d x

integral of sqrt((5x)/4)

\int \frac{5 x}{4} d x

integral of be^{-bx}

\int b e^{- b x} d x

integral of (2x+1)cot^2(x)

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

integral of (1+ln(x))/(x(ln(x))^2)

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

Frequently Asked Questions (FAQ)

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