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Popular >

integral of 3x+x^2y

Solution

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

Solution

\frac{3 x ^{2}}{2} + \frac{y x ^{3}}{3} + C

Solution steps

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

\int 3 x d x = \frac{3 x ^{2}}{2}

\int y x^{2} d x = \frac{y x ^{3}}{3}

= \frac{3 x ^{2}}{2} + \frac{y x ^{3}}{3}

Add a constant to the solution

= \frac{3 x ^{2}}{2} + \frac{y x ^{3}}{3} + C

Popular Examples

derivative of 1/10 (e^{5x}+e^{-5x})derivative of

\frac{1}{10} (e^{5 x} + e^{- 5 x})

derivative of y=sqrt(e^{2x)+x}derivative of

y = e^{2 x} + x

derivative of f(x)=(4x)/(x+1)derivative of

f (x) = \frac{4 x}{x + 1}

integral of (x^5)/((8-x^6)^2)

\int \frac{x ^{5}}{( 8 - x ^{6} ) ^{2}} d x

integral of 2/(5x-8)

\int \frac{2}{5 x - 8} d x

Frequently Asked Questions (FAQ)

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