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Popular >

integral of 1+t^2

Solution

\int 1 + t^{2} d t

Solution

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

Solution steps

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

\int 1 d t = t

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

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

Add a constant to the solution

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

Popular Examples

integral of-25sin(-5t)

\int - 25 sin (- 5 t) d t

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

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

derivative of arccos(e^{6x})

\frac{d}{d x} (arccos (e^{6 x}))

integral of (6t^2+4t)(t^3+t^2+1)^6

\int (6 t^{2} + 4 t) (t^{3} + t^{2} + 1)^{6} d t

limit as x approaches-2-of x+2

x \to - 2 - lim (x + 2)

Frequently Asked Questions (FAQ)

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