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Popular >

integral of x^5+x+3

Solution

\int x^{5} + x + 3 d x

Solution

\frac{x ^{6}}{6} + \frac{x ^{2}}{2} + 3 x + C

Solution steps

\int x^{5} + x + 3 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 x d x + \int 3 d x

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

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

\int 3 d x = 3 x

= \frac{x ^{6}}{6} + \frac{x ^{2}}{2} + 3 x

Add a constant to the solution

= \frac{x ^{6}}{6} + \frac{x ^{2}}{2} + 3 x + C

Graph

Popular Examples

integral of x^3-0.3x^2-8.56x+8.448

\int x^{3} - 0.3 x^{2} - 8.56 x + 8.448 d x

integral of (2/x-x)^2

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

integral of 7/(x^2)-2/x

\int \frac{7}{x ^{2}} - \frac{2}{x} d x

integral of sqrt(8x^2+1)

\int 8 x^{2} + 1 d x

integral of (x-1)/(x^{2/3)+x^{1/3}+1}

\int \frac{x - 1}{x ^{\frac{2}{3}} + x ^{\frac{1}{3}} + 1} d x

Frequently Asked Questions (FAQ)

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