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Popular >

integral of 3(x+1)

Solution

\int 3 (x + 1) d x

Solution

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

Solution steps

\int 3 (x + 1) d x

Take the constant out:

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

= 3 \cdot \int x + 1 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

= 3 (\int x d x + \int 1 d x)

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of (t^3)/3+1

\int \frac{t ^{3}}{3} + 1 d t

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

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

integral of (x+6)/(2x^3-18x)

\int \frac{x + 6}{2 x ^{3} - 18 x} d x

integral of (3x+2)/(x^2+2x+5)

\int \frac{3 x + 2}{x ^{2} + 2 x + 5} d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of 3(x+1) ?
The integral of 3(x+1) is 3((x^2)/2+x)+C