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Popular >

integral of x+e^{5x}

Solution

\int x + e^{5 x} d x

Solution

\frac{x ^{2}}{2} + \frac{1}{5} e^{5 x} + C

Solution steps

\int x + e^{5 x} 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 x d x + \int e^{5 x} d x

\int x d x = \frac{x ^{2}}{2}

\int e^{5 x} d x = \frac{1}{5} e^{5 x}

= \frac{x ^{2}}{2} + \frac{1}{5} e^{5 x}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{1}{5} e^{5 x} + C

Popular Examples

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\int_{0}^{π} f (x) sin (x) d x

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9 y^{^{''}} + 6 y^{^{'}} + 4 y = 0

integral of 2e^t

\int 2 e^{t} d t

area 7cos(9x),7-7cos(9x),0, pi/9 area

7 cos (9 x), 7 - 7 cos (9 x), 0, \frac{π}{9}

Frequently Asked Questions (FAQ)

What is the integral of x+e^{5x} ?
The integral of x+e^{5x} is (x^2)/2+1/5 e^{5x}+C