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Popular >

integral of (3x-1)^2

Solution

\int (3 x - 1)^{2} d x

Solution

3 x^{3} - 3 x^{2} + x + C

Solution steps

\int (3 x - 1)^{2} d x

Expand

(3 x - 1)^{2} : 9 x^{2} - 6 x + 1

= \int 9 x^{2} - 6 x + 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 9 x^{2} d x - \int 6 x d x + \int 1 d x

\int 9 x^{2} d x = 3 x^{3}

\int 6 x d x = 3 x^{2}

\int 1 d x = x

= 3 x^{3} - 3 x^{2} + x

Add a constant to the solution

= 3 x^{3} - 3 x^{2} + x + C

Popular Examples

integral of cos(8x)

\int cos (8 x) d x

f(x)=e^xsqrt(x)

f (x) = e^{x} x

integral of (sqrt(x^2-36))/(x^3)

\int \frac{x ^{2} - 36}{x ^{3}} d x

y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 11

integral of 5tan(2x)ln(cos(2x))

\int 5 tan (2 x) ln (cos (2 x)) d x

Frequently Asked Questions (FAQ)

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