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Popular >

integral of (5x+2)^2

Solution

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

Solution

\frac{25 x ^{3}}{3} + 10 x^{2} + 4 x + C

Solution steps

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

Expand

(5 x + 2)^{2} : 25 x^{2} + 20 x + 4

= \int 25 x^{2} + 20 x + 4 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 25 x^{2} d x + \int 20 x d x + \int 4 d x

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

\int 20 x d x = 10 x^{2}

\int 4 d x = 4 x

= \frac{25 x ^{3}}{3} + 10 x^{2} + 4 x

Add a constant to the solution

= \frac{25 x ^{3}}{3} + 10 x^{2} + 4 x + C

Popular Examples

integral from 0 to 1 of 2pix(x-x^2)

\int_{0}^{1} 2 π x (x - x^{2}) d x

y^{''}+10y=0,y(0)=2,y^'(0)=10

y^{^{''}} + 10 y = 0, y (0) = 2, y^{^{'}} (0) = 10

integral of tan^7(x)sec^{17}(x)

\int tan^{7} (x) sec^{17} (x) d x

derivative of s(t)= 1/(t^2+6t-7)derivative of

s (t) = \frac{1}{t ^{2} + 6 t - 7}

integral of (ln(4x))/x

\int \frac{ln ( 4 x )}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (5x+2)^2 ?
The integral of (5x+2)^2 is (25x^3)/3+10x^2+4x+C