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Popular >

integral of (x^3+2x)

Solution

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

Solution

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

Solution steps

\int x^{3} + 2 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 2 x d x

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

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

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

Add a constant to the solution

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

Popular Examples

y^{''}+3(y^')^2=-17

y^{^{''}} + 3 (y^{^{'}})^{2} = - 17

integral of-3e^{-3x}

\int - 3 e^{- 3 x} d x

derivative of 7sin(x+7xcos(x))

\frac{d}{d x} (7 sin (x) + 7 x cos (x))

integral of-3y^2

\int - 3 y^{2} d y

integral of t/((1-t^2)^{3/2)}

\int \frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}} d t

Frequently Asked Questions (FAQ)

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