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Popular >

integral of-e^{-t}+1

Solution

\int - e^{- t} + 1 d t

Solution

e^{- t} + t + C

Solution steps

\int - e^{- t} + 1 d t

Apply u-substitution

: \int e^{u} - 1 d u

= \int e^{u} - 1 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{u} d u - \int 1 d u

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

\int 1 d u = u

= e^{u} - u

Substitute back

u = - t

= e^{- t} - (- t)

Simplify

= e^{- t} + t

Add a constant to the solution

= e^{- t} + t + C

Popular Examples

tangent of f(x)=x^4-10x^2+9,\at x=1 tangent of

f (x) = x^{4} - 10 x^{2} + 9, at x = 1

derivative of h(g(x)k(x))derivative of

h (g (x) k (x))

derivative of 2/3 (1+x)^{3/2}derivative of

\frac{2}{3} (1 + x)^{\frac{3}{2}}

tangent of f(x)=3e^x,\at x=0 tangent of

f (x) = 3 e^{x}, at x = 0

y^'=-5y+5t^2+2t,y(0)= 1/3

y^{^{'}} = - 5 y + 5 t^{2} + 2 t, y (0) = \frac{1}{3}

Frequently Asked Questions (FAQ)

What is the integral of-e^{-t}+1 ?
The integral of-e^{-t}+1 is e^{-t}+t+C