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Popular >

integral of (t^2+1)

Solution

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

Solution

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

Solution steps

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

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

\int 1 d t = t

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(2x^3+2x^2y-3y^3)

\frac{\partial}{\partial x} (2 x^{3} + 2 x^{2} y - 3 y^{3})

integral from-10 to 10 of 100-x^2

\int_{- 10}^{10} 100 - x^{2} d x

(dy)/(dx)=x^2sqrt(x-2)

\frac{d y}{d x} = x^{2} x - 2

limit as x approaches 1 of (-5)/(1-x)

x \to 1 lim (\frac{- 5}{1 - x})

integral of 3(2x+5)^3

\int 3 (2 x + 5)^{3} d x

Frequently Asked Questions (FAQ)

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