Solve ∫ 5x*(-2xy)+2x^2*(-2y)+7*(2x^2y)=

$$\int 5 x \cdot ( - 2 x y ) + 2 x ^ { 2 } \cdot ( - 2 y ) + 7 \cdot ( 2 x ^ { 2 } y ) =$$

Evaluate

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Solution Steps

Multiply x and x to get x^{2}.

$$\int 5x^{2}\left(-2\right)y+2x^{2}\left(-2\right)y+7\times 2x^{2}y\mathrm{d}x$$

Multiply 5 and -2 to get -10.

$$\int -10x^{2}y+2x^{2}\left(-2\right)y+7\times 2x^{2}y\mathrm{d}x$$

Multiply 2 and -2 to get -4.

$$\int -10x^{2}y-4x^{2}y+7\times 2x^{2}y\mathrm{d}x$$

Combine -10x^{2}y and -4x^{2}y to get -14x^{2}y.

$$\int -14x^{2}y+7\times 2x^{2}y\mathrm{d}x$$

Multiply 7 and 2 to get 14.

$$\int -14x^{2}y+14x^{2}y\mathrm{d}x$$

Combine -14x^{2}y and 14x^{2}y to get 0.

$$\int 0\mathrm{d}x$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}x=ax.

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If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

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Differentiate w.r.t. x

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