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Popular >

integral of (x/2)^5

Solution

\int (\frac{x}{2})^{5} d x

Solution

\frac{x ^{6}}{192} + C

Solution steps

\int (\frac{x}{2})^{5} d x

Simplify

(\frac{x}{2})^{5} : \frac{x ^{5}}{32}

= \int \frac{x ^{5}}{32} d x

Take the constant out:

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

= \frac{1}{32} \cdot \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= \frac{1}{32} \cdot \frac{x ^{6}}{6}

Simplify

\frac{1}{32} \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{192}

= \frac{x ^{6}}{192}

Add a constant to the solution

= \frac{x ^{6}}{192} + C

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\int \frac{1}{49 + 25 x ^{2}} d x

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\int - sin (x^{3}) d x

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\int (2000 x - 7)^{3} d x

integral of sqrt(2x+3)sin(sqrt(2x+3))

\int 2 x + 3 sin (2 x + 3) d x

Frequently Asked Questions (FAQ)

What is the integral of (x/2)^5 ?
The integral of (x/2)^5 is (x^6)/(192)+C