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Popular >

integral of 5x^2+1

Solution

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

Solution

\frac{5 x ^{3}}{3} + x + C

Solution steps

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 1 d x = x

= \frac{5 x ^{3}}{3} + x

Add a constant to the solution

= \frac{5 x ^{3}}{3} + x + C

Popular Examples

integral from 0 to 3 of xsqrt(x^2+16)

\int_{0}^{3} x x^{2} + 16 d x

derivative of x^2sin(3x-2)

\frac{d}{d x} (x^{2} sin (3 x - 2))

integral from 0 to 1 of 1/x

\int_{0}^{1} \frac{1}{x} d x

derivative of sec^2(x-tan^2(x))

\frac{d}{d x} (sec^{2} (x) - tan^{2} (x))

limit as t approaches 0 of (5^t-3^t)/t

t \to 0 lim (\frac{5 ^{t} - 3 ^{t}}{t})

Frequently Asked Questions (FAQ)

What is the integral of 5x^2+1 ?
The integral of 5x^2+1 is (5x^3)/3+x+C