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Popular >

integral of e^x+x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of-1/7 x+1

\int - \frac{1}{7} x + 1 d x

integral of 1/(sqrt(x^2+3/4))

\int \frac{1}{x ^{2} + \frac{3}{4}} d x

integral of 2e^tt

\int 2 e^{t} t d t

integral of (-6x+18)/((x^2+2x+4)^2)

\int \frac{- 6 x + 18}{( x ^{2} + 2 x + 4 ) ^{2}} d x

integral of-(60)/(x^2)

\int - \frac{60}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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