What is the integral of r^3cos^2(θ) ?

The integral of r^3cos^2(θ) is (r^4cos^2(θ))/4+C

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integral of r^3cos^2(θ)

\int r^{3} cos^{2} (θ) d r

\frac{r ^{4} cos ^{2} ( θ )}{4} + C

Solution steps

\int r^{3} cos^{2} (θ) d r

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos^{2} (θ) \cdot \int r^{3} d r

Apply the Power Rule

: \frac{r ^{4}}{4}

= cos^{2} (θ) \frac{r ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{r ^{4} cos ^{2} ( θ )}{4}

Add a constant to the solution

= \frac{r ^{4} cos ^{2} ( θ )}{4} + C

\int \frac{x ^{3} + 3 x}{x ^{2} - 3 x - 10} d x

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

\int x^{4} \cdot e^{(1 - x^{5})} d x

\int \frac{10}{9 x ^{2}} d x

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

What is the integral of r^3cos^2(θ) ?
The integral of r^3cos^2(θ) is (r^4cos^2(θ))/4+C