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Popular >

integral of x^3+x+1

Solution

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

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

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\int \frac{sin ( x )}{( 1 + cos ^{2} ( x ) )} d x

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\int \frac{4}{x} + e^{- 2 x} d x

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

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

integral of 3xcos^2(x)

\int 3 x cos^{2} (x) d x

integral of b/(sin^2(a)x)

\int \frac{b}{sin ^{2} ( a ) x} d x

Frequently Asked Questions (FAQ)

What is the integral of x^3+x+1 ?
The integral of x^3+x+1 is (x^4)/4+(x^2)/2+x+C