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Popular >

integral of x+x^4

Solution

\int x + x^{4} d x

Solution

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

Solution steps

\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

integral of (x+1)e^{2x+1}

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

integral of 48x^{-1/5}tan(x^{4/5})

\int 48 x^{- \frac{1}{5}} tan (x^{\frac{4}{5}}) d x

integral of 1/(sqrt((1+x^2)*ln(x+\sqrt{1+x^2)))}

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

integral of (x^2-2x-15)

\int (x^{2} - 2 x - 15) d x

integral of 5x^4e^{8x^5}

\int 5 x^{4} e^{8 x^{5}} d x

Frequently Asked Questions (FAQ)

What is the integral of x+x^4 ?
The integral of x+x^4 is (x^2)/2+(x^5)/5+C