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Popular >

integral of (9x+2)^2

Solution

\int (9 x + 2)^{2} d x

Solution

27 x^{3} + 18 x^{2} + 4 x + C

Solution steps

\int (9 x + 2)^{2} d x

Expand

(9 x + 2)^{2} : 81 x^{2} + 36 x + 4

= \int 81 x^{2} + 36 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 81 x^{2} d x + \int 36 x d x + \int 4 d x

\int 81 x^{2} d x = 27 x^{3}

\int 36 x d x = 18 x^{2}

\int 4 d x = 4 x

= 27 x^{3} + 18 x^{2} + 4 x

Add a constant to the solution

= 27 x^{3} + 18 x^{2} + 4 x + C

Popular Examples

integral of (a+bx^5)/(6ax+bx^6)

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

y^{''}+4y^'-24y=0

y^{^{''}} + 4 y^{^{'}} - 24 y = 0

integral of e^x+e^xx

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

derivative of g(x)= 1/(sqrt(x))derivative of

g (x) = \frac{1}{x}

inverse oflaplace 6/s+(16)/(s^2+16)inverse laplace

\frac{6}{s} + \frac{16}{s ^{2} + 16}

Frequently Asked Questions (FAQ)

What is the integral of (9x+2)^2 ?
The integral of (9x+2)^2 is 27x^3+18x^2+4x+C