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Popular Calculus >

integral of x(2+x^5)

Solution

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

Solution

x^{2} + \frac{x ^{7}}{7} + C

Solution steps

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

Expand

x (2 + x^{5}) : 2 x + x^{6}

= \int 2 x + x^{6} 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 2 x d x + \int x^{6} d x

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

\int x^{6} d x = \frac{x ^{7}}{7}

= x^{2} + \frac{x ^{7}}{7}

Add a constant to the solution

= x^{2} + \frac{x ^{7}}{7} + C

Graph

Popular Examples

integral of (r^3+5)^2

\int (r^{3} + 5)^{2} d r

integral of (2y-2)

\int (2 y - 2) d y

integral of (x^4+1)/(x^3+3x^2+2x)

\int \frac{x ^{4} + 1}{x ^{3} + 3 x ^{2} + 2 x} d x

integral of (x+7)/(sqrt(4-(x-2)^2))

\int \frac{x + 7}{4 - ( x - 2 ) ^{2}} d x

integral of (x^{3/2}+8)^5sqrt(x)

\int (x^{\frac{3}{2}} + 8)^{5} x d x

Frequently Asked Questions (FAQ)

What is the integral of x(2+x^5) ?
The integral of x(2+x^5) is x^2+(x^7)/7+C