en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (t^2)/(at^3-b)

Solution

\int \frac{t ^{2}}{a t ^{3} - b} d t

Solution

\frac{1}{3 a} ln - b + a t^{3} + C

Solution steps

\int \frac{t ^{2}}{a t ^{3} - b} d t

Apply u-substitution

: \int \frac{1}{3 a u} d u

= \int \frac{1}{3 a u} d u

Take the constant out:

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

= \frac{1}{3 a} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3 a} ln ∣ u ∣

Substitute back

u = - b + a t^{3}

= \frac{1}{3 a} ln - b + a t^{3}

Add a constant to the solution

= \frac{1}{3 a} ln - b + a t^{3} + C

Popular Examples

integral of 70csc^2(θ)

\int 70 csc^{2} (θ) d θ

integral of (5x+3)^6

\int (5 x + 3)^{6} d x

integral of x^2*sqrt(1+x^3)

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

integral of 4bc

\int 4 b c d x

integral of 1/(-x^2+2x+1)

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

Frequently Asked Questions (FAQ)

What is the integral of (t^2)/(at^3-b) ?
The integral of (t^2)/(at^3-b) is 1/(3a)ln|-b+at^3|+C