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Popular >

integral of 5e^x+x^3

Solution

\int 5 e^{x} + x^{3} d x

Solution

5 e^{x} + \frac{x ^{4}}{4} + C

Solution steps

\int 5 e^{x} + x^{3} 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 5 e^{x} d x + \int x^{3} d x

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

\int x^{3} d x = \frac{x ^{4}}{4}

= 5 e^{x} + \frac{x ^{4}}{4}

Add a constant to the solution

= 5 e^{x} + \frac{x ^{4}}{4} + C

Popular Examples

integral of (e^{xy}+xye^{xy})

\int (e^{x y} + x y e^{x y}) d x

integral of 5x^3(x^4-3)

\int 5 x^{3} (x^{4} - 3) d x

integral of 4cos(x+4y)+ze^{yz}

\int 4 cos (x + 4 y) + z e^{yz} d y

integral of (1-x)cos(x)

\int (1 - x) cos (x) d x

integral of x^5(x^2+1)^2

\int x^{5} (x^{2} + 1)^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 5e^x+x^3 ?
The integral of 5e^x+x^3 is 5e^x+(x^4)/4+C