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Popular >

integral of (n+3)3

Solution

\int (n + 3) 3 d n

Solution

3 (\frac{n ^{2}}{2} + 3 n) + C

Solution steps

\int (n + 3) \cdot 3 d n

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int n + 3 d n

Apply the Sum Rule:

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

= 3 (\int n d n + \int 3 d n)

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

\int 3 d n = 3 n

= 3 (\frac{n ^{2}}{2} + 3 n)

Add a constant to the solution

= 3 (\frac{n ^{2}}{2} + 3 n) + C

Popular Examples

integral of 2/(e^x+2)

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

tangent of f(x)=(36x)/(x^2+36),\at x=-3 tangent of

f (x) = \frac{36 x}{x ^{2} + 36}, at x = - 3

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

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

(\partial)/(\partial x)(e^{3x}cos(4x))

\frac{\partial}{\partial x} (e^{3 x} cos (4 x))

d/(dt)(3+3cos(t^3)-4sin(t^3))

\frac{d}{d t} (3 + 3 cos (t^{3}) - 4 sin (t^{3}))

Frequently Asked Questions (FAQ)

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