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Popular >

integral of 2x^3+2

Solution

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

Solution

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

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of x^3ln(sqrt(x))

\int x^{3} ln (x) d x

integral of (5pi)/(x^4)

\int \frac{5 π}{x ^{4}} d x

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

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

integral of t/(t^2+2)

\int \frac{t}{t ^{2} + 2} d t

integral of sin(1+3x)

\int sin (1 + 3 x) d x

Frequently Asked Questions (FAQ)

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