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Popular >

integral of (2t^2+1)

Solution

\int (2 t^{2} + 1) d t

Solution

\frac{2 t ^{3}}{3} + t + C

Solution steps

\int 2 t^{2} + 1 d t

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 t^{2} d t + \int 1 d t

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

\int 1 d t = t

= \frac{2 t ^{3}}{3} + t

Add a constant to the solution

= \frac{2 t ^{3}}{3} + t + C

Popular Examples

integral of r*e^{r/2}

\int r \cdot e^{\frac{r}{2}} d r

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

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

integral of 2sqrt(2x+3)

\int 2 2 x + 3 d x

integral of ((x+1))/(x^2+4x-5)

\int \frac{( x + 1 )}{x ^{2} + 4 x - 5} d x

integral of (x^2-2x+3)/(x^2+4)

\int \frac{x ^{2} - 2 x + 3}{x ^{2} + 4} d x

Frequently Asked Questions (FAQ)

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