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Popular >

integral of x^2+7x-5

Solution

\int x^{2} + 7 x - 5 d x

Solution

\frac{x ^{3}}{3} + \frac{7 x ^{2}}{2} - 5 x + C

Solution steps

\int x^{2} + 7 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 7 x d x - \int 5 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 5 d x = 5 x

= \frac{x ^{3}}{3} + \frac{7 x ^{2}}{2} - 5 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{7 x ^{2}}{2} - 5 x + C

Popular Examples

integral of 1/(sin^5(x))

\int \frac{1}{sin ^{5} ( x )} d x

(\partial)/(\partial x)(cos^2(3x-y^2))

\frac{\partial}{\partial x} (cos^{2} (3 x - y^{2}))

derivative of f(x)=sqrt(x)+1/(sqrt(x^3))derivative of

f (x) = x + \frac{1}{x ^{3}}

area x=2y,x=y^2-3 area

x = 2 y, x = y^{2} - 3

integral of 2x^2+5x

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

Frequently Asked Questions (FAQ)

What is the integral of x^2+7x-5 ?
The integral of x^2+7x-5 is (x^3)/3+(7x^2)/2-5x+C