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Popular >

integral of 5x^5-x

Solution

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

Solution

\frac{5 x ^{6}}{6} - \frac{x ^{2}}{2} + C

Solution steps

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

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

\int x d x = \frac{x ^{2}}{2}

= \frac{5 x ^{6}}{6} - \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{5 x ^{6}}{6} - \frac{x ^{2}}{2} + C

Popular Examples

integral of sec^9(x)

\int sec^{9} (x) d x

integral from 0 to 1 of ln(t)

\int_{0}^{1} ln (t) d t

(\partial)/(\partial x)(2x^{1/2}+y)

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}} + y)

derivative of f(x)=sqrt(9x+7)derivative of

f (x) = 9 x + 7

integral of 3/(6+3x)

\int \frac{3}{6 + 3 x} d x

Frequently Asked Questions (FAQ)

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