What is the integral from x^3 to x+1 of (3x+2y) ?

The integral from x^3 to x+1 of (3x+2y) is -x^6-3x^4+4x^2+5x+1

Popular >

integral from x^3 to x+1 of (3x+2y)

\int_{x^{3}}^{x + 1} (3 x + 2 y) d y

- x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

Solution steps

\int_{x^{3}}^{x + 1} 3 x + 2 y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{x^{3}}^{1 + x} 2 y d y + \int_{x^{3}}^{1 + x} 3 x d y

\int_{x^{3}}^{1 + x} 2 y d y = (1 + x)^{2} - x^{6}

\int_{x^{3}}^{1 + x} 3 x d y = 3 x (1 + x) - 3 x^{4}

= (1 + x)^{2} - x^{6} + 3 x (1 + x) - 3 x^{4}

Simplify

(1 + x)^{2} - x^{6} + 3 x (1 + x) - 3 x^{4} : - x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

= - x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

\int_{0}^{3} (x 9 - x^{2}) d x

\int_{\frac{π}{4}}^{π} sin^{2} (x) d x

\int_{0}^{π} cos (2 x) sin (2 x) d x

\int_{2 π}^{4 π} sin (x) d x

\int_{0}^{3} \frac{8}{( 1 + x ) ^{2}} d x

What is the integral from x^3 to x+1 of (3x+2y) ?
The integral from x^3 to x+1 of (3x+2y) is -x^6-3x^4+4x^2+5x+1