What is the integral from x to x^3 of y/x ?

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

Popular >

integral from x to x^3 of y/x

\int_{x}^{x^{3}} \frac{y}{x} d y

\frac{x ( x ^{4} - 1 )}{2}

Solution steps

\int_{x}^{x^{3}} \frac{y}{x} d y

Take the constant out:

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

= \frac{1}{x} \cdot \int_{x}^{x^{3}} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{x}^{x^{3}}

= \frac{1}{x} [\frac{y ^{2}}{2}]_{x}^{x^{3}}

Simplify

\frac{1}{x} [\frac{y ^{2}}{2}]_{x}^{x^{3}} : \frac{[ \frac{y ^{2}}{2} ] _{x}^{x^{3}}}{x}

= \frac{[ \frac{y ^{2}}{2} ] _{x}^{x^{3}}}{x}

Compute the boundaries:

\frac{x ^{6}}{2} - \frac{x ^{2}}{2}

= \frac{\frac{x ^{6}}{2} - \frac{x ^{2}}{2}}{x}

Simplify

= \frac{x ( x ^{4} - 1 )}{2}

\int_{1}^{\infty} \frac{1}{x ^{m}} d x

\int_{2}^{6} 6 x d x

\int_{0}^{x} t^{2} e^{t^{2}} d t

\int_{0}^{a} x e^{\frac{x}{a}} d x

\int_{0}^{4} 17 d x

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