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Popular >

integral of xarctag(x)

Solution

\int x a rc t a g (x) d x

Solution

\frac{a ^{2} cr t g x ^{3}}{3} + C

Solution steps

\int x a rc t a gx d x

Take the constant out:

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

= aa cr t g \cdot \int xx d x

Simplify

aa cr t g : a^{2} cr t g

= a^{2} cr t g \cdot \int xx d x

Simplify

xx : x^{2}

= a^{2} cr t g \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= a^{2} cr t g \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{a ^{2} cr t g x ^{3}}{3}

Add a constant to the solution

= \frac{a ^{2} cr t g x ^{3}}{3} + C

Popular Examples

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\int (x + 4) 4 - x d x

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\int (x^{3} + 2 x - 7) d x

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\int x^{8} cos (x^{9}) d x

integral of cot^2(3x)*csc^4(3x)

\int cot^{2} (3 x) \cdot csc^{4} (3 x) d x

integral of tan^8(x)sec^8(x)

\int tan^{8} (x) sec^{8} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of xarctag(x) ?
The integral of xarctag(x) is (a^2crtgx^3)/3+C