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Popular >

integral of x(1+x^3)

Solution

\int x (1 + x^{3}) d x

Solution

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

Solution steps

\int x (1 + x^{3}) d x

Expand

x (1 + x^{3}) : x + x^{4}

= \int x + x^{4} 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 d x + \int x^{4} d x

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

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

= \frac{x ^{2}}{2} + \frac{x ^{5}}{5}

Add a constant to the solution

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

Popular Examples

y^{^{'}} + y = 2, y (0) = 0

slope of (-5.3)(7.9)slope

(- 5.3) (7.9)

integral from 0 to 1 of 5xe^{-x^2}

\int_{0}^{1} 5 x e^{- x^{2}} d x

x^2y^{''}=2xy^'+(y^')^2

x^{2} y^{^{''}} = 2 x y^{^{'}} + (y^{^{'}})^{2}

tangent of f(x)=x^2+8,(1,9)tangent of

f (x) = x^{2} + 8, (1, 9)

Frequently Asked Questions (FAQ)

What is the integral of x(1+x^3) ?
The integral of x(1+x^3) is (x^2)/2+(x^5)/5+C