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Popular >

integral of x^2+4x+5

Solution

\int x^{2} + 4 x + 5 d x

Solution

\frac{x ^{3}}{3} + 2 x^{2} + 5 x + C

Solution steps

\int x^{2} + 4 x + 5 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^{2} d x + \int 4 x d x + \int 5 d x

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

\int 4 x d x = 2 x^{2}

\int 5 d x = 5 x

= \frac{x ^{3}}{3} + 2 x^{2} + 5 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x^{2} + 5 x + C

Popular Examples

ydy=4xsqrt(y^2+1)dx

y d y = 4 x y^{2} + 1 d x

(dy)/(dx)=(x^2+y^2)/(x^2)

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{x ^{2}}

(x/(x^2+y^4))dx+(((2y^3))/(x^2+y^4))dy=0

(\frac{x}{x ^{2} + y ^{4}}) d x + (\frac{( 2 y ^{3} )}{x ^{2} + y ^{4}}) d y = 0

derivative of (7x^3+x/(6sqrt(x)))

\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})

derivative of log_{10}(1/x)

\frac{d}{d x} (lo g_{10} (\frac{1}{x}))

Frequently Asked Questions (FAQ)

What is the integral of x^2+4x+5 ?
The integral of x^2+4x+5 is (x^3)/3+2x^2+5x+C