What is the integral from cos(x) to e^x of x^2 ?

The integral from cos(x) to e^x of x^2 is (e^{3x}-cos^3(x))/3

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integral from cos(x) to e^x of x^2

\int_{c o s (x)}^{e^{x}} x^{2} d x

\frac{e ^{3 x} - cos ^{3} ( x )}{3}

Solution steps

\int_{c o s (x)}^{e^{x}} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{c o s (x)}^{e^{x}}

= [\frac{x ^{3}}{3}]_{c o s (x)}^{e^{x}}

Compute the boundaries:

\frac{1}{3} e^{3 x} - \frac{cos ^{3} ( x )}{3}

= \frac{1}{3} e^{3 x} - \frac{cos ^{3} ( x )}{3}

Simplify

= \frac{e ^{3 x} - cos ^{3} ( x )}{3}

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\int_{2}^{5} ln (x^{2} - 2) d x

\int_{0}^{l n (x)} (x e^{- y}) d y

\int_{- \infty}^{2} e^{- 5 x} d x

What is the integral from cos(x) to e^x of x^2 ?
The integral from cos(x) to e^x of x^2 is (e^{3x}-cos^3(x))/3