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Popular >

integral of t^2+e^t

Solution

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

Solution

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

Solution steps

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

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

\int e^{t} d t = e^{t}

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

Add a constant to the solution

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

Popular Examples

integral of x^3e^{4x}

\int x^{3} e^{4 x} d x

integral from 0 to pi of 9sin^2(4x)

\int_{0}^{π} 9 sin^{2} (4 x) d x

limit as x approaches 0 of sin^3(2x)

x \to 0 lim (sin^{3} (2 x))

derivative of (-8x/((x^2-16)^2))

\frac{d}{d x} (\frac{- 8 x}{( x ^{2} - 16 ) ^{2}})

(\partial)/(\partial x)(e^{-x-3y})

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

Frequently Asked Questions (FAQ)

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