Question

Evaluate the function w.r.t.x $\int (3 x^{2} -5)^{2}dx$

Answer 1

this is the answer of this question

Answer 2

Answer:

$\dfrac {9x^5}5 + 25x -{10x^3}+C$

Step-by-step explanation:

We have to find the integration of $\int (3x^2 - 5)^2 dx$

So,

$\int (3x^2 -5)^2 dx$

By the formula of $(a - b)^2$

${(a-b)^2 = a^2 +b^2 -2ab}$

$(3x^2 - 5)^2 = (3x^2)^2 + 5^2 - 2 \times 3x^2 \times 5\\(3x^2 - 5)^2 = 9x^4 + 25 - 30x^2$

$\int (9x^4 + 25 -30x^2)dx\\9\int x^4dx + 25\int dx - 30\int x^2dx$

$\dfrac {9x^5}5 + 25x -{10x^3}+C$