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Popular >

integral of x^5-1

Solution

\int x^{5} - 1 d x

Solution

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

Solution steps

\int x^{5} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{5} d x - \int 1 d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of (3x^2-4x+2)e^x

\int (3 x^{2} - 4 x + 2) e^{x} d x

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\int \frac{1}{x ^{2} - 4 x - 21} d x

integral of (2x)/((1-x^2)^2)

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

integral of 5/(e^{4x)}

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

integral of (x-76)/(x^2(x+4))

\int \frac{x - 76}{x ^{2} ( x + 4 )} d x

Frequently Asked Questions (FAQ)

What is the integral of x^5-1 ?
The integral of x^5-1 is (x^6)/6-x+C