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Popular >

integral of (4x+7)^2

Solution

\int (4 x + 7)^{2} d x

Solution

\frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C

Solution steps

\int (4 x + 7)^{2} d x

Expand

(4 x + 7)^{2} : 16 x^{2} + 56 x + 49

= \int 16 x^{2} + 56 x + 49 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 16 x^{2} d x + \int 56 x d x + \int 49 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 56 x d x = 28 x^{2}

\int 49 d x = 49 x

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x

Add a constant to the solution

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C

Popular Examples

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\int \frac{x ^{2} + 1}{x ^{3} + 3 x + 4} d x

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\int \frac{3 x - 4}{x ^{2} - 1} d x

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\int \frac{d}{1} (v) d x

integral of cot^2(2x)csc^2(2x)

\int cot^{2} (2 x) csc^{2} (2 x) d x

integral of 1/((x+3)(x-2))

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

Frequently Asked Questions (FAQ)

What is the integral of (4x+7)^2 ?
The integral of (4x+7)^2 is (16x^3)/3+28x^2+49x+C