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Popular >

integral of (x^3+x)

Solution

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

Solution

\frac{x ^{4}}{4} + \frac{x ^{2}}{2} + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{x ^{2}}{2} + C

Popular Examples

integral of (18x^2+3)(6x^3+3x)^6

\int (18 x^{2} + 3) (6 x^{3} + 3 x)^{6} d x

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

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

slope of f(x)=4^x slope

f (x) = 4^{x}

y = x^{4 x}

integral of xtanh^2(x)

\int x tanh^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of (x^3+x) ?
The integral of (x^3+x) is (x^4)/4+(x^2)/2+C