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Popular >

integral of y^3+3y

Solution

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

Solution

\frac{y ^{4}}{4} + \frac{3 y ^{2}}{2} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y^{3} d y + \int 3 y d y

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

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

= \frac{y ^{4}}{4} + \frac{3 y ^{2}}{2}

Add a constant to the solution

= \frac{y ^{4}}{4} + \frac{3 y ^{2}}{2} + C

Popular Examples

integral of (2x)/(3(x-1)(x+1)^2)

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

integral of (sqrt(y))/(sqrt(y^3+4))

\int \frac{y}{y ^{3} + 4} d y

integral of 6/(sqrt(25-16t^2))

\int \frac{6}{25 - 16 t ^{2}} d t

integral of (2x+8)/((x^2+2x+5)^2)

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

integral of 16x^7e^{2x^4}

\int 16 x^{7} e^{2 x^{4}} d x

Frequently Asked Questions (FAQ)

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