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Popular >

integral of e^{3x}+1

Solution

\int e^{3 x} + 1 d x

Solution

\frac{1}{3} e^{3 x} + x + C

Solution steps

\int e^{3 x} + 1 d x

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^{3 x} d x + \int 1 d x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

\int 1 d x = x

= \frac{1}{3} e^{3 x} + x

Add a constant to the solution

= \frac{1}{3} e^{3 x} + x + C

Popular Examples

integral of 12x+24x^2

\int 12 x + 24 x^{2} d x

y^{^{'}} - y = e^{x} y^{2}

derivative of (x-43/(sqrt(x)-\sqrt{43)})

\frac{d}{d x} (\frac{x - 43}{x - 43})

integral of 6sin^4(xco)s^2x

\int 6 sin^{4} (x co) s^{2} x d x

limit as x approaches 0+of d^2y

x \to 0 + lim (d^{2} y)

Frequently Asked Questions (FAQ)

What is the integral of e^{3x}+1 ?
The integral of e^{3x}+1 is 1/3 e^{3x}+x+C