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Popular Calculus >

integral of-3x^5

Solution

\int - 3 x^{5} d x

Solution

- \frac{x ^{6}}{2} + C

Solution steps

\int - 3 x^{5} d x

Take the constant out:

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

= - 3 \cdot \int x^{5} d x

Apply the Power Rule

= - 3 \cdot \frac{x ^{6}}{6}

Simplify

- 3 \cdot \frac{x ^{6}}{6} : - \frac{x ^{6}}{2}

= - \frac{x ^{6}}{2}

Add a constant to the solution

= - \frac{x ^{6}}{2} + C

Graph

Popular Examples

derivative of arccot(sqrt(x^2+1))

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

integral of e^{7x+2}

\int e^{7 x + 2} d x

derivative of (3x^2+2^2(x^2-5x)^3)

\frac{d}{d x} ((3 x^{2} + 2)^{2} (x^{2} - 5 x)^{3})

(\partial)/(\partial x)(6x^2+11y)

\frac{\partial}{\partial x} (6 x^{2} + 11 y)

integral of 1/(81e^{-5x)+e^{5x}}

\int \frac{1}{81 e ^{- 5 x} + e ^{5 x}} d x

Frequently Asked Questions (FAQ)

What is the integral of-3x^5 ?
The integral of-3x^5 is -(x^6)/2+C